I think I'll coin some numbers in the Fibonacci sequence, using BEAF.
Fibonacci-un = {3} = 3 (to prevent degeneration into 1 or 4) (Class 0)
Fibonacci-duo = {3, 5} = 3^5 = 243 (Class 1)
Fibonacci-tri = {3, 5, 8} = 3 {8} 5 (Class 7: Up-arrow notation level)
Fibonacci-tet = {3, 5, 8, 13} (Class 8: Linear omega level)
Fibonacci-pent = {3, 5, 8, 13, 21} (Class 9: Quadratic omega level)
Fibonacci-hex = {3, 5, 8, 13, 21, 34} (Class 10: Polynomial omega level)
Fibonacci-hept = {3, 5, 8, 13, 21, 34, 55} (Class 10: Polynomial omega level)
Fibonacci-oct = {3, 5, 8, 13, 21, 34, 55, 89} (Class 10: Polynomial omega level)
Fibonacci-enn = {3, 5, 8, 13, 21, 34, 55, 89, 144} (Class 10: Polynomial omega level)
Fibonacci-deck = {3, 5, 8, 13, 21, 34, 55, 89, 144, 233} (Class 10: Polynomial omega level)
Fibonacci-endeck = {3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377} (Class 10: Polynomial omega level)
Fibonacci-dodeck = {3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610} (Class 10: Polynomial omega level)
Fibonacci-triadeck = {3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987} (Class 10: Polynomial omega level)
Fibonacci-tetradeck = {3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597} (Class 10: Polynomial omega level)
Fibonacci-pentadeck = {3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584} (Class 10: Polynomial omega level)
Fibonacci-hexadeck = {3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181} (Class 10: Polynomial omega level)
Dimen-Fibonacci-hex = {3, 5 (8) 13} (Class 12: Exponentiated polynomial omega level)
Superdimen-Fibonacci-hept = {3, 5 (8, 13) 21} (Class 13: Double exponentiated polynomial omega level)
Hyperdimen-Fibonacci-hept = {3, 5 ((8)13) 21} (Class 14: Triple exponentiated polynomial omega level)