A392103 - OEIS

A392103

E.g.f. A(x) satisfies A(x) = (1 + 5*x*A(x)^2)^(1/5).

1, 1, 0, -6, 24, 216, -4032, 0, 943488, -11176704, -242694144, 9527341824, 0, -7499076609024, 147882278928384, 5095578094903296, -305111521320173568, 0, 508176786181510397952, -14025066012671465816064, -662064303879059808190464, 53300612668336707221323776, 0

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OFFSET

0,4

LINKS

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

FORMULA

a(n) = 5^n * n! * binomial((2*n+1)/5,n)/(2*n+1).

a(5*n+2) = 0.

MATHEMATICA

a[n_]:=If[n==0, 1, Product[(2*n+1-5*k), {k, 0, n-1}]/(2*n+1)]; Table[a[n], {n, 0, 20}] (* Vincenzo Librandi, Mar 26 2026 *)

PROG

(PARI) a(n) = 5^n*n!*binomial((2*n+1)/5, n)/(2*n+1);