A361607 a(n) = n! * Sum_{k=0..n} binomial(n+(n-1)*k,n*k)/k!.

1, 2, 9, 88, 1457, 35226, 1158097, 49554464, 2664907233, 175012404562, 13725980234201, 1263867766626312, 134795551989905809, 16464112185873351338, 2280346417134518709537, 355060682992984062716176

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = n! * [x^n] exp( x/(1-x)^n ) / (1-x).

a(n) = Sum_{k=0..n} (n*k+n-k)!/(n*k)! * binomial(n,k).

log(a(n)) ~ n*(2*log(n) - log(log(n)) - 1 - log(2) + (log(log(n)) + log(2) + 1/2)/log(n)). - Vaclav Kotesovec, Mar 17 2023

Mathematica

Table[Sum[Binomial[n, k]*(n*k + n - k)!/(n*k)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 17 2023 *)

Prog

(PARI) a(n) = sum(k=0, n, (n*k+n-k)!/(n*k)!*binomial(n, k));

Crossrefs

Main diagonal of A361600.

Cf. A293013.

Sequence in context: A347013 A132431 A228509 * A001192 A006120 A012941

Adjacent sequences: A361604 A361605 A361606 * A361608 A361609 A361610

Keyword

nonn

Author

Seiichi Manyama, Mar 17 2023

Status

approved