A383120 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n*k,k).

1, 2, 11, 139, 2885, 82381, 2979565, 130203494, 6664589321, 390857822425, 25832193906761, 1899273577364197, 153741850998047053, 13585520026454056279, 1301210398133681268381, 134270617908678099820891, 14849785991790603714043921, 1752283118795349858851381297

Offset: 0

Author

Ilya Gutkovskiy, Apr 17 2025

Keywords

• nonn

Crossrefs

Cf. A001850, A014062, A026375, A188686, A226391, A359643, A378327, A383121.

Programs

Mathematica

Table[Sum[Binomial[n, k] Binomial[n k, k], {k, 0, n}], {n, 0, 17}]

PARI

a(n) = sum(k=0, n, binomial(n,k) * binomial(n*k,k)); \\ Michel Marcus, Apr 17 2025

Formula

a(n) = [x^n] ((1 + x)^n + x)^n.

a(n) ~ exp(n + exp(-1) - 1/2) * n^n / sqrt(2*Pi*n). - Vaclav Kotesovec, Apr 17 2025