A388532 Expansion of (1/x) * Series_Reversion( x / ((1+x)^5 + x^2) ).

1, 5, 36, 300, 2722, 26101, 260190, 2669462, 28002249, 298963196, 3237960822, 35488918800, 392888868903, 4387005861750, 49349543809305, 558734798970563, 6362099356555975, 72809587673936221, 837020276958155372, 9661490726164235205, 111929162083852179336

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..916

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+1,k) * binomial(5*n-5*k+5,n-2*k).

a(n) = (1/(n+1)) * [x^n] ((1+x)^5 + x^2)^(n+1).

Mathematica

Table[(1/(n+1)) Coefficient[((1+x)^5+x^2)^(n+1), x, n], {n, 0, 20}] (* Vincenzo Librandi, Sep 30 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^5+x^2))/x)
(PARI) a(n) = sum(k=0, n\2, binomial(n+1, k)*binomial(5*n-5*k+5, n-2*k))/(n+1);
(Magma) R<x> := PolynomialRing(Rationals()); [ (1/(n+1))*Coefficient(((1+x)^5 + x^2)^(n+1), n) : n in [0..20] ]; // Vincenzo Librandi, Sep 30 2025

Crossrefs

Cf. A065065, A071356, A369213, A388538.

Cf. A364748.

Sequence in context: A255489 A091161 A390780 * A364765 A135149 A269007

Adjacent sequences: A388529 A388530 A388531 * A388533 A388534 A388535

Keyword

nonn

Author

Seiichi Manyama, Sep 18 2025

Status

approved