A378461 a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(2*n+2*k-1,n-k).

1, 2, 16, 137, 1216, 11057, 102229, 956601, 9032680, 85893860, 821402341, 7891371303, 76105710253, 736364519399, 7144586617597, 69487754788517, 677259385478616, 6613163312601491, 64681617534027028, 633569272646345064, 6214190349161222941, 61023489213944162889

Offset

0,2

Links

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

Formula

a(n) = [x^n] 1/(1 - x - x/(1 - x)^2)^n.

Mathematica

Table[Sum[Binomial[n+k-1, k] * Binomial[2*n+2*k-1, n-k], {k, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Jun 06 2026 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(2*n+2*k-1, n-k));

Crossrefs

Cf. A009723, A378460.

Cf. A378466.

Sequence in context: A001252 A067058 A002302 * A348803 A369580 A056662

Adjacent sequences: A378458 A378459 A378460 * A378462 A378463 A378464

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2024

Status

approved