A066382 a(n) = Sum_{k=0..n} binomial(n^2,k).

1, 2, 11, 130, 2517, 68406, 2391496, 102022810, 5130659561, 296881218694, 19415908147836, 1415538531617772, 113796709835547767, 9998149029974754104, 952980844872975079232, 97930011125976327934826, 10791878598088498089377489, 1269466214540655412954317894

Offset: 0

Author

N. J. A. Sloane, Dec 23 2001

Keywords

• nonn
• changed

Links

• Harry J. Smith, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A206849.

Programs

Magma

[&+[Binomial(n^2, k): k in [0..n]]: n in [0..20]]; // Vincenzo Librandi, Jun 08 2019

Mathematica

Table[Sum[Binomial[n^2, k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Jun 08 2019 *)

PARI

{ for (n=0, 100, a=0; for (k=0, n, a+=binomial(n^2, k)); write("b066382.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 12 2010

PARI

a(n) = sum(k=0, n, binomial(n^2,k)); \\ Michel Marcus, Jun 08 2019

Formula

a(n) = 2^(n^2) - binomial(n^2, n+1)*hypergeom([1, -n^2+n+1], [2+n], -1). - Vladeta Jovovic, Jul 08 2003

a(n) ~ exp(n - 1/2) * n^(n - 1/2) / sqrt(2*Pi). - Vaclav Kotesovec, Jun 07 2019