A389294 Expansion of (1/x) * Series_Reversion( x * (1 - x^2 * (1 + x)^2) ).

1, 0, 1, 2, 4, 14, 36, 108, 335, 1012, 3211, 10192, 32683, 106216, 346800, 1141482, 3779784, 12577620, 42064286, 141258502, 476183950, 1610841570, 5466208800, 18602676690, 63476386506, 217122438096, 744346687756, 2557117326080, 8801719487108, 30350690178528

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

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

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

Mathematica

Table[SeriesCoefficient[1/(1-x^2*(1+x)^2)^(n+1), {x, 0, n}]/(n+1), {n, 0, 30}] (* Vincenzo Librandi, Oct 19 2025 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1-x^2*(1+x)^2))/x)
(Magma) [1/(n+1)*&+[Binomial(n+k, k)*Binomial(2*k, n-2*k): k in [0..Floor(n/2)]]: n in [0..35]]; // Vincenzo Librandi, Oct 19 2025

Crossrefs

Cf. A214372, A389062, A389292.

Sequence in context: A088028 A327459 A336108 * A263739 A333892 A135960

Adjacent sequences: A389291 A389292 A389293 * A389295 A389296 A389297

Keyword

nonn

Author

Seiichi Manyama, Sep 28 2025

Status

approved