A392128 - OEIS

A392128

E.g.f. A(x) satisfies A(x) = (1 + 5*x*A(x)^3)^(1/5).

1, 1, 2, 0, -48, -264, 3024, 68544, 0, -21700224, -290594304, 7038130176, 304874938368, 0, -284964911142912, -6063173436063744, 224205436175745024, 14340241502048157696, 0, -26933369667620051091456, -785403696709602085699584, 39061793928864528683237376, 3304637985436875847722074112, 0

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OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..350

FORMULA

a(n) = 5^n * n! * binomial((3*n+1)/5,n)/(3*n+1).

a(5*n+3) = 0.

MATHEMATICA

a[n_]:=If[n==0, 1, Product[(3* n+1-5 *k), {k, 0, n-1}]/(3 *n+1)]; Table[a[n], {n, 0, 25}] (* Vincenzo Librandi, Mar 26 2026 *)

PROG

(PARI) a(n) = 5^n*n!*binomial((3*n+1)/5, n)/(3*n+1);