A306241 a(n) = Sum_{k=0..n} (k*n)!/n!^k.

1, 2, 8, 1702, 63097722, 623372476627154, 2670179107513625597282318, 7363615751879726008424500256018442794, 18165723935734974232438957032838329596079311234990642

Offset

0,2

Links

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

Formula

a(n) equals (row sums of A120666) + 1.

From Vaclav Kotesovec, Feb 08 2019: (Start)

a(n) ~ A034841(n).

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

Mathematica

Table[Sum[(k*n)!/n!^k, {k, 0, n}], {n, 0, 10}] (* Vaclav Kotesovec, Feb 08 2019 *)

Prog

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

Crossrefs

Cf. A120666, A221177.

Sequence in context: A027668 A121015 A216619 * A073630 A027733 A054874

Adjacent sequences: A306238 A306239 A306240 * A306242 A306243 A306244

Keyword

nonn

Author

Seiichi Manyama, Jan 31 2019

Status

approved