A377195 - OEIS

A377195

Expansion of 1/(1 - 4*x*(1+x)^2)^(5/2).

1, 10, 90, 710, 5250, 37072, 253330, 1688640, 11039370, 71049200, 451429880, 2837585940, 17674206130, 109224234420, 670398280520, 4090210956596, 24823230801450, 149941593205140, 901881446152120, 5404072772837620, 32269536034506456, 192087243952281920

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(0) = 1, a(1) = 10, a(2) = 90; a(n) = (2*(2*n+3)*a(n-1) + 8*(n+3)*a(n-2) + 2*(2*n+9)*a(n-3))/n.

a(n) = Sum_{k=0..n} (-4)^k * binomial(-5/2,k) * binomial(2*k,n-k).

MATHEMATICA

a[n_]:=Sum[(-4)^k*Binomial[-5/2, k]Binomial[2*k, n-k], {k, 0, n}]; Array[a, 22, 0] (* Stefano Spezia, May 08 2025 *)

PROG

(PARI) a(n) = sum(k=0, n, (-4)^k*binomial(-5/2, k)*binomial(2*k, n-k));