A394495 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - 5*x)^(1/5) ).

1, 1, 8, 126, 3000, 96096, 3877632, 188972784, 10801574784, 708750000000, 52514194876416, 4337146638849024, 395110823965304832, 39360597010307629056, 4256752500000000000000, 496690565175807256590336, 62197673632104828591341568, 8320198233259787899473985536

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

E.g.f. A(x) satisfies A(x) = 1/(1 - 5*x*A(x))^(1/5).

a(n) = 5^n * n! * binomial((6*n-4)/5,n)/(n+1).

a(n) ~ 6^(6*n/5-3/10)*exp(-n)*n^(n-1). - Stefano Spezia, Mar 22 2026

Mathematica

a[n_]:=5^n*n!*Binomial[(6 n-4)/5, n]/(n+1); Table[a[n], {n, 0, 20}] (* Vincenzo Librandi, Mar 30 2026 *)

Prog

(PARI) a(n) = 5^n*n!*binomial((6*n-4)/5, n)/(n+1);
(Magma) [1] cat [5^n*Factorial(n)*&*[((6*n-4)/5-k): k in [0..n-1]]/Factorial(n)/(n+1): n in [1..20]]; // Vincenzo Librandi, Mar 30 2026

Crossrefs

Cf. A000142, A001761, A282626, A385369, A385440, A393169, A394494.

Sequence in context: A360852 A262732 A220728 * A355766 A029472 A001081

Adjacent sequences: A394492 A394493 A394494 * A394496 A394497 A394498

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 22 2026

Status

approved