A306206 a(n) = Sum_{k=0..n} (n^2)!/((n^2-n*k)!*n!^k).

1, 2, 13, 3445, 127028721, 1249195963773451, 5343245431687763366112193, 14729376926426500067331714992293420777, 36332859343341728199556523379140726537646663631786369

Offset: 0

Author

Seiichi Manyama, Jan 29 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..26

Crossrefs

Cf. A206849, A227403, A306207.

Programs

PARI

{a(n) = sum(k=0, n, (n^2)!/((n^2-n*k)!*n!^k))}

Formula

From Vaclav Kotesovec, Jan 29 2019: (Start)

a(n) ~ 2 * (n^2)! / (n!)^n.

a(n) ~ n^(n^2 - n/2 + 1) / (exp(1/12) * 2^((n-3)/2) * Pi^((n-1)/2)). (End)