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A306241 a(n) = Sum_{k=0..n} (k*n)!/n!^k. 1
1, 2, 8, 1702, 63097722, 623372476627154, 2670179107513625597282318, 7363615751879726008424500256018442794, 18165723935734974232438957032838329596079311234990642 (list; graph; refs; listen; history; text; internal format)
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: A014116 A121015 A216619 * A073630 A027733 A054874

Adjacent sequences:  A306238 A306239 A306240 * A306242 A306243 A306244

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jan 31 2019

STATUS

approved

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Last modified November 14 14:43 EST 2019. Contains 329126 sequences. (Running on oeis4.)