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%I #21 Sep 08 2022 08:45:04
%S 1,2,11,130,2517,68406,2391496,102022810,5130659561,296881218694,
%T 19415908147836,1415538531617772,113796709835547767,
%U 9998149029974754104,952980844872975079232,97930011125976327934826,10791878598088498089377489,1269466214540655412954317894
%N a(n) = Sum_{k=0..n} binomial(n^2,k).
%H Harry J. Smith, <a href="/A066382/b066382.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = 2^(n^2) - binomial(n^2, n+1)*hypergeom([1, -n^2+n+1], [2+n], -1). - _Vladeta Jovovic_, Jul 08 2003
%F a(n) ~ exp(n - 1/2) * n^(n - 1/2) / sqrt(2*Pi). - _Vaclav Kotesovec_, Jun 07 2019
%t Table[Sum[Binomial[n^2, k], {k, 0, n}], {n, 0, 20}] (* _Vincenzo Librandi_, Jun 08 2019 *)
%o (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
%o (PARI) a(n) = sum(k=0, n, binomial(n^2,k)); \\ _Michel Marcus_, Jun 08 2019
%o (Magma) [&+[Binomial(n^2, k): k in [0..n]]: n in [0..20]]; // _Vincenzo Librandi_, Jun 08 2019
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Dec 23 2001
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