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

0,3

Links

Table of n, a(n) for n=0..13.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A007820, A350376, A351507.

Sequence in context: A049003 A268961 A196422 * A248703 A264903 A003281

Adjacent sequences: A351505 A351506 A351507 * A351509 A351510 A351511

Keyword

nonn

Author

Seiichi Manyama, Feb 12 2022

Status

approved