A378567 a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n+3*k-1,n-k).

1, 1, 11, 88, 715, 5951, 50288, 429696, 3702987, 32125390, 280211701, 2454992618, 21588647392, 190444368401, 1684556756320, 14935618142768, 132695019071499, 1181070210132582, 10529299131757754, 94005323670592130, 840373149466892965, 7521508912742542806

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = [x^n] 1/(1 - x/(1 - x)^4)^n.

Mathematica

a[n_]:=SeriesCoefficient[ 1/(1 - x/(1 - x)^4)^n, {x, 0, n}]; Array[a, 22, 0] (* Stefano Spezia, Dec 01 2024 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(n+3*k-1, n-k));

Crossrefs

Cf. A002002, A378565, A378566.

Cf. A055991, A367234.

Sequence in context: A224179 A037601 A037706 * A175605 A162576 A142166

Adjacent sequences: A378564 A378565 A378566 * A378568 A378569 A378570

Keyword

nonn

Author

Seiichi Manyama, Dec 01 2024

Status

approved