A389130 Expansion of (1/x) * Series_Reversion( x / (1 + x^4 * (1 + x)^2) ).

1, 0, 0, 0, 1, 2, 1, 0, 4, 18, 30, 22, 28, 156, 455, 700, 740, 1632, 5763, 13566, 20919, 30590, 76615, 216062, 453882, 743820, 1351480, 3381300, 8346195, 16673202, 29670480, 60714864, 146619708, 334010864, 660718872, 1267177824, 2738125060, 6363431976

Offset

0,6

Links

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+1,k) * binomial(2*k,n-4*k).

a(n) = (1/(n+1)) * [x^n] (1 + x^4 * (1 + x)^2)^(n+1).

Mathematica

Table[(1/(n+1)) Coefficient[(1+x^4*(1+x)^2)^(n+1), x, n], {n, 0, 35}] (* Vincenzo Librandi, Sep 28 2025 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x/(1+x^4*(1+x)^2))/x)
(Magma) R<x> := PolynomialRing(Rationals()); [ (1/(n+1))*Coefficient(((1 + x^4 * (1 + x)^2)^(n+1)), n) : n in [0..30] ]; // Vincenzo Librandi, Sep 28 2025

Crossrefs

Cf. A389129.

Sequence in context: A185411 A254882 A086095 * A322119 A363731 A112334

Adjacent sequences: A389127 A389128 A389129 * A389131 A389132 A389133

Keyword

nonn

Author

Seiichi Manyama, Sep 24 2025

Status

approved