A351507 a(n) = [x^n] Product_{k=1..n} (1 + k*x)^n.

1, 1, 13, 630, 65446, 11732175, 3222746276, 1257489289280, 661150527657180, 450529025613124095, 386183537239831846450, 406654820487854059966416, 516014868401631381045209376, 776565429016998902169538130936

Offset

0,3

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000142, A129256, A351508.

Sequence in context: A374605 A372243 A362862 * A067407 A143734 A362898

Adjacent sequences: A351504 A351505 A351506 * A351508 A351509 A351510

Keyword

nonn

Author

Seiichi Manyama, Feb 12 2022

Status

approved