A306207 - OEIS

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A306207

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

1, 2, 19, 9745, 768211081, 17406784944114721, 179762725526880242306609281, 1230064011299573560897489169488350806401, 7660929590740297929124296619236388608530015362840364161

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

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)

PROG

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

CROSSREFS