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A066382 a(n) = Sum_{k=0..n} binomial(n^2,k). 3
1, 2, 11, 130, 2517, 68406, 2391496, 102022810, 5130659561, 296881218694, 19415908147836, 1415538531617772, 113796709835547767, 9998149029974754104, 952980844872975079232, 97930011125976327934826, 10791878598088498089377489, 1269466214540655412954317894 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
MATHEMATICA
Table[Sum[Binomial[n^2, k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Jun 08 2019 *)
PROG
(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
(Magma) [&+[Binomial(n^2, k): k in [0..n]]: n in [0..20]]; // Vincenzo Librandi, Jun 08 2019
CROSSREFS
Sequence in context: A283537 A154596 A337458 * A276030 A282855 A139387
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 23 2001
STATUS
approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)