A387774 - OEIS

A387774

Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x^3*(1+x)^2)) ).

1, 2, 5, 15, 54, 223, 992, 4560, 21290, 100529, 480060, 2318802, 11321625, 55805869, 277312150, 1387534268, 6983733054, 35333320780, 179592533802, 916638589151, 4696157366880, 24141943779719, 124496020737875, 643838254787444, 3338370481991835, 17351586033841827, 90388143128099199

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

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

a(n) = (1/(n+1)) * [x^n] ((1+x)^2 * (1+x^3*(1+x)^2))^(n+1).

MATHEMATICA

Table[SeriesCoefficient[((1+x)^2*(1+x^3*(1+x)^2))^(n+1), {x, 0, n}]/(n+1), {n, 0, 30}] (* Vincenzo Librandi, Oct 20 2025 *)

PROG

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