A361880 - OEIS

A361880

Expansion of 1/(1 - 9*x/(1 - x)^2)^(1/3).

1, 3, 24, 207, 1893, 17952, 174402, 1723494, 17250000, 174354822, 1776119970, 18208500000, 187659221409, 1942674634371, 20187543581880, 210472842939975, 2200677521078253, 23068297001178240, 242353695578011416, 2551260130246575048, 26905595698893121728

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OFFSET

0,2

LINKS

Winston de Greef, Table of n, a(n) for n = 0..961

FORMULA

a(n) = Sum_{k=0..n} (-9)^k * binomial(-1/3,k) * binomial(n+k-1,n-k).

a(0) = 1; a(n) = (3/n) * Sum_{k=0..n-1} (n+2*k) * (n-k) * a(k).

(n-1)*n*a(n) = (11*n-6)*(n-1)*a(n-1) - 18*(n-2)*a(n-2) - (11*n-38)*(n-3)*a(n-3) + (n-3)*(n-4)*a(n-4) for n > 3.

a(n) ~ 3^(1/3) * ((11 + 3*sqrt(13))/2)^n / (Gamma(1/3) * 13^(1/6) * n^(2/3)). - Vaclav Kotesovec, Mar 28 2023

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-9*x/(1-x)^2)^(1/3))