A378326 a(n) = Sum_{k=0..n} binomial(n-1,k-1) * binomial(n*k,k) / ((n-1)*k+1).

1, 1, 3, 19, 219, 3901, 95838, 3022909, 116798643, 5350403737, 283728025998, 17104314563843, 1155635807408096, 86513627563199279, 7109252862969177287, 636268582522962837475, 61610670571434193189443, 6418044336586421956746033, 715718717341021991299583730

Offset: 0

Author

Vaclav Kotesovec, Nov 23 2024

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..338

Crossrefs

Cf. A002212, A307678, A349331, A349332, A349333, A349334, A349335.

Cf. A377098, A378325, A378327.

Programs

Mathematica

Table[Sum[Binomial[n-1, k-1]*Binomial[n*k, k]/((n-1)*k+1), {k, 0, n}], {n, 0, 20}]

Formula

a(n) ~ exp(n + exp(-1) - 1/2) * n^(n - 5/2) / sqrt(2*Pi).