1. really evil number = 666↓(Φ↑(666↓(Φ↑(666)),0,0)),0,0 (in Evil Matrix Notation), where ↑ is superscript, and ↓ is subscript.

2. supreme evil number = SPE(6,6,6) (in Evil Matrix Notation)

3. Lunar Seven = P↑7_↓7_(7↓𝜑↑0.7_) (in Penumbral Termination), where ↑ is superscript,_ is going back to normal script, and ↓ is subscript.

4. Googoldeciphaplex = [x,x -lim-> 9,10], x = 10 -> 10 -> (in Chained Array Notation)

5. Umbral Googol = P↑10↑100_↓10↑100_(10↑100_↓𝜑↑0.8_) (in Penumbral Termination), where ↑ is superscript, _ is going back to ` script, and ↓ is subscript.

6. Umbral Googolplex = 10↑`P↑10↑100_↓10↑100_(10↑100_↓𝜑↑0.8_) (in Penumbral Termination), where ↑ is superscript,` is setting script point, _ is going back to ` script, and ↓ is subscript.

7. Magnificent 8 = P↑(8 -> 8 -> 8)_↓(8 -> 8 -> 8)_((8 -> 8 -> 8)↓𝜑↑0.8_)↑`P↑8_↓8_(8↓𝜑↑0.8_) (in Penumbral Termination and Chained Arrow Notation), where ↑ is superscript,` is setting script point, _ is going back to ` script, and ↓ is subscript.

8. Megadeca = Boxed 10 Finalized (in Staged Array Notation)

9. Webinarr = \{ [^{〈〈〈〈}\ {'} \ ^{〉〉〉〉}2^{100}] ,2^{100} \} (in Staged Array Notation) (in LaTeX)

10. Pirytillion = Π^(3) (1#^(4)1) (in Extended Pie Scale)

11. Denholm = Q^{64}(1024) (using the Q Function) (in LaTeX)

12. Muphi = f^{2}_{\mu}(100) (in Fast-Growing Hierarchy) (in LaTeX)

13. Tatsujin = nu^2^2(2) = nu^4(2) (using the Binary Extremity Function)

This is not a series of numbers, this is a list of every ordinal I have coined. All of these are formatted in LaTeX.

1.  Denholm's Ordinal (ס) = \omega\&^{\omega}[\omega]!

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For more information of these 6 ordinals, see this page.

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2.  Suttner (\Lambda_{n}) = \alpha\mapsto \overset{n+1}{\overbrace{\omega\uparrow ^{\omega\uparrow ^{\cdot^{\cdot^{\cdot^{\omega\uparrow ^{\omega}\alpha}\alpha}}}\alpha}\alpha}}=\alpha\mapsto \omega\uparrow ^{\Lambda_{(n-1)}}\alpha

3.  Baus (\nu_{n}) = \alpha\mapsto \Lambda_{0}\uparrow ^{\nu_{(n-1)}}\alpha

4.  Small Nachtnebel Ordinal (\chi_{0}) = \vartheta_{0}(\omega)

5.  Large Nachtnebel Ordinal (\varkappa_{n}) = \underset{\omega}{\underbrace{\vartheta_{0}(\vartheta_{0}(\cdots(\vartheta_{0}(}}\omega\underset{\omega}{\underbrace{)\cdots)))}}

6.  Superhuge Nachtnebel Ordinal (\beta_{n}) = \small\text{least Nachtnebel Ordinal unreachable by the Nachtnebel Ordinal Identifier Function}

7.  Transnachtnebel Ordinal (\mathfrak{N}^{\mathfrak{T}}_{n}) = \text{The furthest possible countable Inaccessible Nachtnebel Ordinal}

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These next ones have a subscript 0 on them. In the case of these ones, each time you add 1 to the 0, it acts as the next solution to its value, just like the epsilon numbers! 

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8. Theta-Null (\vartheta_{0}) =\alpha\mapsto \eta_{\alpha}=\varphi(4,0)

9. Pi-Cipher (\Pi_{0}) =\alpha\mapsto \vartheta_{\alpha}=\varphi(5,0)

10. Pi-Nil (\varpi_{0}) =\alpha\mapsto \Pi_{\alpha}=\varphi(6,0)

11. Mu-Naught (\mu_{0}) =\alpha\mapsto (\beta\mapsto (\gamma\mapsto (\delta\mapsto \varpi_{\delta})_{\gamma})_{\beta})_{\alpha}=\varphi(10,0)

1.  Iridellion = 1/(10(^*355450)10)

2.  Hemocillion = 1/(10(^*777)10)

3.  Kaltillion = 1/(10^3.62)

4.  Eradephillion = 10^3.62

5.  Hemoglobcidillion = 10(^*777)10

6.  Coruscatillion = 10(^*355450)10

7.  Fjorillion = 10(^*(10^100))10

8.  Iodinillion = 10(^*(10^^3))10

9.  Pragmagillion = 10(^*(10^10^100))10

10.  Guildillion = 10 > 10 > (10 > 10 > 10)

11.  Tempillion = 10 > 10 > (10 > 10 > (10 > 10 > 10))

(10 > 10 > = ς - First Step Chroma

12.  Sivillion = 10ς 10

13.  Cursillion = (10 > 10 > (10 > 10 > 10))ς 10

14.  Yillion = 10ς * ς 10

15.  Fictillion = 10^10ς * ς 10

16.  Gophillion = 10^^10ς * ς 10

17.  Tyranillion = ς^3 10

18.  Nathillion = ς^4 10

19.  Sillyillion = ς^10 10

20.  Cleansillion = ς^^2 10

21.  Swillion = ς^^3 10

22.  Platinumillion = ς^^4 10

23.  Flowlinillion = ς^^10 10

24.  Scintillion = (ς 10) > 15 > 2

25.  Intillion = (ς 10) > 10 > 3

26.  Fuchsillion = (ς 10) > 10 > 10

((ς 10) > (ς 10) > = ϱ - Step 2 Chroma 

27.  Teratomatillion = 10ϱ 10

28.  Thermillion = (ϱ 10) > 10 > 10

29.  Temptillion = (10ϱ 10) > 10 > 10

30.  Clowillion = (10ϱ 10) > (10ϱ 10) > (10ϱ 10)

((777ϱ 10) > (777ϱ 10) > = ξ - Step 3 Chroma

31.  Xinillion = ξ^^10 10

32.  Omillion = (ξ^^10 10) > (ξ^^10 10) > (ξ^^10 10)

33.  Zentillion = ((ξ 10) > 10 > 10) > ((ξ 10) > 10 > 10) > ((ξ 10) > 10 > 10)

(((ξ^^^10 10) > (ξ^^^10 10) > (ξ^^^10 10)) > ((ξ^^^10 10) > (ξ^^^10 10) > (ξ^^^10 10)) > = ϖ - Step 4 Chroma

34.  Cognillion = ϖ^^^^10 10

35.  Umbracillion = (ϖ 10) > 10 > ((ϖ 10) > 10 > 10)

(((ϖ^^^^100 10) > (ϖ^^^^100 10) > (ϖ^^^^100 10)) > ((ϖ^^^^100 10) > (ϖ^^^^100 10) > (ϖ^^^^100 10)) > = Ꮳ (Chromatic C) - Final Step Chroma

36.  Chromationed C = Ꮳ 100

37.  Chromaticillion = (Ꮳ 100 ^^^^^ ϖ 10 ^^^^ ξ 10 ^^^ ϱ 10 ^^ ς ^ 10) > (Ꮳ 100 ^^^^^ ϖ 10 ^^^^ ξ 10 ^^^ ϱ 10 ^^ ς ^ 10) > (Ꮳ 777 > Ꮳ 777 > Ꮳ 777)

Note that this is not a series, it is just a list of numbers using my DRAGONLADY notation.

1.  Monolemna = [1] = 1

2.  Bilemna = [2] = 2↑^(2↑2)2 = 2↑^(4)2 = 2↑↑↑↑2 = 4

3. Trilemna = [3] = 3↑^(3↑^(3↑3)3)3 = 3↑^(3↑^(27)3)3

4.  Pentalemna = [5] = 5↑^(5↑^(5↑^(5↑^(5↑5)5)5)5)5

5.  Decalemna = [10] = 10↑^(10↑^(10↑^(10↑^(10↑^(10↑^(10↑^(10↑^(10↑^(10↑10)10)10)10)10)10)10)10)10)10

6.  Centilemna = [100]

7.  Googolemna = [10^100]

8.  Decaphotil = #[10]

9.  Megaphotil = #[10^6]

10.  Biquadathriphotil = #+4[2]

11.  Decadecamultiphotil = 10#[10]

12.  Googolemnaphotil = [#][10^100]

13.  Googolemnaphotilplex = 10^([#][10^100])

14.  Centidecamegielphotil = 10¬[100]

15.  Septaseptaseptamegielphotil = 7¬^(7)[7]

16.  Septaseptaseptaseptaseptaseptaseptaseptaseptamegielphotilmultiphotilmultiphotilmultiphotil = (((7¬^(7)[7])#[7])#[7]))#[7]

17.  Decadecadecamegielphotildecadecadecamegielphotildecadecadecamegielphotilmegielphotil = (10¬^(10)[10])¬^(10¬^(10)[10])[(10¬^(10)[10])]

18. Decadecadecamegielphotildecadecadecamegielphotildecadecadecamegielphotilmegielphotildecadecadecamegielphotildecadecadecamegielphotildecadecadecamegielphotilmegielphotildecadecadecamegielphotildecadecadecamegielphotildecadecadecamegielphotilmegielphotilmegielphotildecadecadecamegielphotildecadecadecamegielphotildecadecadecamegielphotilmegielphotildecadecadecamegielphotildecadecadecamegielphotildecadecadecamegielphotilmegielphotildecadecadecamegielphotildecadecadecamegielphotildecadecadecamegielphotilmegielphotilmegielphotildecadecadecamegielphotildecadecadecamegielphotildecadecadecamegielphotilmegielphotildecadecadecamegielphotildecadecadecamegielphotildecadecadecamegielphotilmegielphotildecadecadecamegielphotildecadecadecamegielphotildecadecadecamegielphotilmegielphotilmegielphotilmegielphotil = ((10¬^(10)[10])¬^(10¬^(10)[10])[(10¬^(10)[10])]¬^((10¬^(10)[10])¬^(10¬^(10)[10])[(10¬^(10)[10])])[(10¬^(10)[10])¬^(10¬^(10)[10])[(10¬^(10)[10])]])¬^((10¬^(10)[10])¬^(10¬^(10)[10])[(10¬^(10)[10])]¬^((10¬^(10)[10])¬^(10¬^(10)[10])[(10¬^(10)[10])])[(10¬^(10)[10])¬^(10¬^(10)[10])[(10¬^(10)[10])]])[((10¬^(10)[10])¬^(10¬^(10)[10])[(10¬^(10)[10])]¬^((10¬^(10)[10])¬^(10¬^(10)[10])[(10¬^(10)[10])])[(10¬^(10)[10])¬^(10¬^(10)[10])[(10¬^(10)[10])]])]

Note that this is NOT a series.

1.  Lucky Factorial = 777! = 179748879246347885915390254860985772110015202277158670755309939319894806008168727526267708821422332676995997017676655042834360729320031150808295761857269193222722736908228562360430531917430683666632570222637491886342891005178166452255929290766202815166868099727085062921134723861984281263470438486775377764574804977158490659002461730632837921146589368499153923601384860240012216365386908982665938676611128958377736237604122271449244811261399030607698653040451128726973937074455818005055743195427492913029767926117779231475248380699706040636827629261705723793684679525708285489082794811185492056733837067876601909494011883579509346537494166015100353712270785582807294006621380202585218713107741889389684517792692361754490413593606781738612659933352419839346158785426492364253430891798558468354200622536432107188204231063100653136983812868581297723204641506540435042036088921769769759837462719765617643231735533115916772664458797084156515865555504650900497620523910098016694353927747171911162967143494305053884052549765045805051906911671070417458619310818909018941774927955558132144776408395187873807144075449621718887770329266691414943153892239059066901063691873780797743177448721177187594863956254648413430376265224016968697513838513387787070380052763935745877645520102494355487949483362369840853003107478344952745043550080983430227746257760016135135678251427617541862082804978298494462381855936995337013589399406284668020494916715104379258663804869970568553096999877031371685655171306907062741195479261795783795298891842550084230458675903367919362696344009558965486868532248434814042685233471036391696092962299446509330110793434267332628028375261381053689528757938477909592102876970504149518352004186637552637014179840000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

2.  Binary-guppyspekt = 1024Δ (bouncing factorial)

3.  Graset = (!10)! (Upper Factorial + Factorial)

4.  Bajillion = 10!^10!^10!

5.  Bifactorillion = 16!^16!^16!^16!^16!^16!^16!^16!^16!^16!^16!^16!^16!^16!^16!^16! (in Nested Factorial Notation)

6.  Actumn = 10&[10]! (in Factorial Array Notation)

7. Denholm's Ordinal (ס) = ω&^ω[ω]! (in Factorial Array Notation)

All are in LaTeX

\text{Bicloek}-\rho(2) \\ \text{Tricloek}-\rho(3) \\ \text{Quadracloek}-\rho(4) \\ \text{Heptacloek}-\rho(7) \\ \text{Decacloek}-\rho(10) \\ \text{Googolcloek}-\rho(10^{100}) \\ \text{Googolplexcloek}-\rho(10^{10^{100}}) \\ \text{Googolcloekplex}-10^{\rho(10^{100})} \\ \text{Tritrihypercloek}-\rho^{3}(3)=\rho(\rho(\rho(3))) \\ \text{Clogol}-\rho^{100}(10)=\underset{100}{\underbrace{\rho(\cdots(\rho(10)\cdots)}} \\ \text{Clogolplex}-\rho^{10^{100}}(10)=\underset{10^{100}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}} \\ \text{Clogolduplex}-\rho^{10^{10^{100}}}(10)=\underset{10^{10^{100}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}} \\ \text{Clogoltriplex}-\rho^{10^{10^{10^{100}}}}(10)=\underset{10^{10^{10^{100}}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}} \\ \text{Deckercloek}-\rho^{10\uparrow \uparrow 9}(10)=\underset{10\uparrow \uparrow 9}{\underbrace{\rho(\cdots(\rho(10)\cdots)}} \\ \text{Tridecide}-\rho_{(2,1)}(3)=\underset{\rho(3)}{\underbrace{\rho(\cdots(\rho(3)\cdots)}} \\ \text{Teradecide}-\rho_{(2,1)}(10^{12})=\underset{\rho(10^{12})}{\underbrace{\rho(\cdots(\rho(10^{12})\cdots)}} \\ \text{Quadhyperdecide}-\rho_{(3,1)}(4)=\underset{\underset{\rho(4)}{\underbrace{\rho(\cdots(\rho(4)\cdots)}}}{\underbrace{\rho(\cdots(\rho(4)\cdots)}} \\ \text{Degol}-\rho_{(3,1)}(10^{100})=\underset{\underset{\rho(10^{100})}{\underbrace{\rho(\cdots(\rho(10^{100})\cdots)}}}{\underbrace{\rho(\cdots(\rho(10^{100})\cdots)}} \\ \text{Acidic Googol}-\rho_{(10,1)}(100)=\underset{\underset{\underset{\underset{\underset{\underset{\underset{\underset{\underset{\Large\rho(100)}{\large\underbrace{\rho(\cdots(\rho(100)\cdots)}}}{ \underbrace{\rho(\cdots(\rho(100)\cdots)}}}{\small \underbrace{\rho(\cdots(\rho(100)\cdots)}}}{\small \underbrace{\rho(\cdots(\rho(100)\cdots)}}}{\small \underbrace{\rho(\cdots(\rho(100)\cdots)}}}{\small \underbrace{\rho(\cdots(\rho(100)\cdots)}}}{\underbrace{\rho(\cdots(\rho(100)\cdots)}}}{\underbrace{\rho(\cdots(\rho(100)\cdots)}}}{\underbrace{\rho(\cdots(\rho(100)\cdots)}} \\ \text{Caustic Googol}-\rho_{(100,1)}(10)=100\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(100)\cdots)}}}{\underbrace{\rho(\cdots(\rho(100)\cdots)}}\end{array} \right. \\ \text{Jovoamosaterahyperdecide}-\rho_{(10^{72},1)}(10^{21})=10^{72}\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10^{21})\cdots)}}}{\underbrace{\rho(\cdots(\rho(10^{21})\cdots)}}\end{array} \right. \\ \text{Millettachalliahyperdecide}-\rho_{(10^{3000},1)}(10^{3000})=10^{3000}\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10^{3000})\cdots)}}}{\underbrace{\rho(\cdots(\rho(10^{3000})\cdots)}}\end{array} \right. \\ \text{Rho}-\overset{\rho(10)}{\overbrace{\rho_{(\rho_{(\rho_{\cdot_{\cdot_{\cdot_{(\rho_{(1,1)}(10),1)}}}}(10),1)}(10),1)}(10)}}=\underset{\rho(10)}{\underbrace{\rho(10)\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.\cdots\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.}} \\ \text{Megarho}- \rho(10) \left\{ \begin{array}{cl} \underset{ \underset{\huge\vdots}{\underbrace{\rho(10)\left\{ \begin{array}{cl} \underset{\underset{\large\vdots}{\underbrace{\rho(10)\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.\cdots\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.}}}{\underbrace{\rho(10)\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.\cdots\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.}} \end{array} \right. \cdots \left\{ \begin{array}{cl} \underset{\underset{\large\vdots}{\underbrace{\rho(10)\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.\cdots\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.}}}{\underbrace{\rho(10)\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.\cdots\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.}} \end{array} \right.}}}{\underbrace{\rho(10)\left\{ \begin{array}{cl} \underset{\underset{\large\vdots}{\underbrace{\rho(10)\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.\cdots\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.}}}{\underbrace{\rho(10)\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.\cdots\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.}} \end{array} \right. \cdots \left\{ \begin{array}{cl} \underset{\underset{\large\vdots}{\underbrace{\rho(10)\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.\cdots\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.}}}{\underbrace{\rho(10)\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.\cdots\left\{ \begin{array}{cl} \underset{\underset{\Large\vdots}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}}{\underbrace{\rho(\cdots(\rho(10)\cdots)}}\end{array} \right.}} \end{array} \right.}} \end{array} \right.

I hope you like these numbers.