A391177 Expansion of (g/(1 - x*g))^4, where g = 1+x*g^3 is the g.f. of A001764.

1, 8, 48, 268, 1480, 8244, 46578, 267080, 1552548, 9135440, 54329890, 326126592, 1973632551, 12029574900, 73786289340, 455130176136, 2821430875502, 17569293911160, 109849736418062, 689347656556720, 4340388605476875, 27412243339811644, 173610555221374102

Offset

0,2

Links

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

Formula

a(n) = 4 * Sum_{k=0..n} binomial(k+4,4) * binomial(3*n-2*k+4,n-k)/(3*n-2*k+4).

Mathematica

Table[4*Sum[Binomial[k+4, 4]*Binomial[3*n-2*k+4, n-k]/(3*n-2*k+4), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 05 2025 *)

Prog

(PARI) a(n) = 4*sum(k=0, n, binomial(k+4, 4)*binomial(3*n-2*k+4, n-k)/(3*n-2*k+4));
(Magma) [4 * &+[Binomial(k+4, 4) * Binomial(3*n-2*k+4, n-k)/(3*n-2*k+4): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Dec 05 2025

Crossrefs

Cf. A391170, A391173, A391176.

Cf. A098746, A391171, A391175.

Cf. A001764.

Sequence in context: A128734 A006321 A371620 * A295047 A295375 A081554

Adjacent sequences: A391174 A391175 A391176 * A391178 A391179 A391180

Keyword

nonn

Author

Seiichi Manyama, Dec 01 2025

Status

approved