A221177 Row sums of A141906.

1, 2, 9, 1777, 63435145, 623666451641641, 2670266572530016805342641, 7363629673367015952858629874317363281, 18165725639381578540715992641519758891553446152650241, 53130688923813417393347555772148839841537612656804852891837024804533761

Offset: 0

Author

N. J. A. Sloane, Jan 05 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20

Crossrefs

Cf. A141906.

Programs

Maple

a:= n-> add((n*m)!/m!^n, m=0..n):
seq(a(n), n=0..10);  # Alois P. Heinz, Jan 09 2013

Mathematica

a[n_] := Sum[(n*m)!/m!^n, {m, 0, n}]; Array[a, 10, 0] (* Jean-François Alcover, Feb 17 2016 *)

PARI

a(n) = sum(m=0, n, (n*m)!/(m!)^n); \\ Michel Marcus, Feb 17 2016

Formula

a(n) ~ n^(n^2 - n/2 + 1) / (exp(1/12) * (2*Pi)^((n-1)/2)). - Vaclav Kotesovec, Feb 08 2019