A306207 a(n) = Sum_{k=0..n} (n^2)!/((n^2-n*k)!*k!^n).
1, 2, 19, 9745, 768211081, 17406784944114721, 179762725526880242306609281, 1230064011299573560897489169488350806401, 7660929590740297929124296619236388608530015362840364161
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..26
Programs
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PARI
{a(n) = sum(k=0, n, (n^2)!/((n^2-n*k)!*k!^n))}
Formula
From Vaclav Kotesovec, Jan 29 2019: (Start)
a(n) ~ (n^2)! / (n! * ((n-1)!)^n).
a(n) ~ exp(n - 1/12) * n^(n^2 - n/2 + 1/2) / (2*Pi)^(n/2). (End)