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

0,2

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

Cf. A206849, A227403, A306206.

Sequence in context: A094663 A274762 A091688 * A355466 A073444 A301637

Adjacent sequences: A306204 A306205 A306206 * A306208 A306209 A306210

Keyword

nonn

Author

Seiichi Manyama, Jan 29 2019

Status

approved