A383120 - OEIS

%I #11 Apr 17 2025 14:54:49

%S 1,2,11,139,2885,82381,2979565,130203494,6664589321,390857822425,

%T 25832193906761,1899273577364197,153741850998047053,

%U 13585520026454056279,1301210398133681268381,134270617908678099820891,14849785991790603714043921,1752283118795349858851381297

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

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

%F a(n) ~ exp(n + exp(-1) - 1/2) * n^n / sqrt(2*Pi*n). - _Vaclav Kotesovec_, Apr 17 2025

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

%o (PARI) a(n) = sum(k=0, n, binomial(n,k) * binomial(n*k,k)); \\ _Michel Marcus_, Apr 17 2025

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

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 17 2025