A378327 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n*k,k) / ((n-1)*k + 1).

1, 2, 5, 25, 257, 4361, 104425, 3241316, 123865313, 5628753361, 296671566941, 17798975341467, 1197924420178381, 89394126594968755, 7326377073291002147, 654215578855903951141, 63225054646397348577601, 6575059243843086616460321, 732138834180570978286488133

Offset: 0

Author

Vaclav Kotesovec, Nov 23 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A007317, A007556, A188687, A346646, A346647, A346648, A346649, A346650.

Cf. A378326.

Programs

Mathematica

Table[Sum[Binomial[n, k] 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).