A391176 Expansion of g^3/(1 - x*g)^4, where g = 1+x*g^3 is the g.f. of A001764.

1, 7, 38, 197, 1030, 5509, 30186, 169050, 964610, 5591855, 32852000, 195207661, 1171258431, 7086855039, 43194471330, 264964662351, 1634592855354, 10134952564820, 63124026093260, 394759553809985, 2477806147246675, 15604618936201007, 98574249230521162

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

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

Prog

(PARI) a(n) = sum(k=0, n, (k+3)*binomial(k+3, 3)*binomial(3*n-2*k+3, n-k)/(3*n-2*k+3));

Crossrefs

Cf. A001764, A391174, A391175, A391178.

Sequence in context: A141845 A048437 A099461 * A104553 A027241 A292761

Adjacent sequences: A391173 A391174 A391175 * A391177 A391178 A391179

Keyword

nonn

Author

Seiichi Manyama, Dec 01 2025

Status

approved