A351508 a(n) = [x^n] Product_{k=1..n} 1/(1 - k*x)^n.

1, 1, 23, 1386, 162154, 31354800, 9078595483, 3682549444112, 1994756395887972, 1391788744738729470, 1216130179327397765925, 1301126343608005909401330, 1673298722590019165433540916, 2547164111922284803722749855516

Offset: 0

Author

Seiichi Manyama, Feb 12 2022

Keywords

• nonn

Crossrefs

Cf. A007820, A350376, A383862, A384060.

Cf. A351507, A384060.

Programs

Mathematica

Table[SeriesCoefficient[Product[1/(1 - k*x)^n, {k,1,n}], {x,0,n}], {n,0,20}] (* Vaclav Kotesovec, Feb 18 2022 *)

PARI

a(n) = polcoef(1/prod(k=1, n, 1-k*x+x*O(x^n))^n, n);

Formula

a(n) ~ exp(n + 5/3) * n^(2*n - 1/2) / (sqrt(Pi) * 2^(n + 1/2)). - Vaclav Kotesovec, Feb 18 2022

a(n) = Sum_{x_1, x_2,..., x_n >= 0 and x_1 + x_2 + ... + x_n = n} Product_{k=1..n} Stirling2(x_k + n,n). - Seiichi Manyama, May 18 2025