A351764 a(n) = [x^n] Product_{k=1..n} (1 + k*x)^n / (1 - k*x)^n.

1, 2, 72, 7848, 1728000, 641258850, 360403076376, 285818177146208, 304172586944446464, 418400927094822149970, 722587619114932445325000, 1530927286486636135080191736, 3904621941927926455303092180480, 11801667653769333351640692783069714

Offset: 0

Author

Vaclav Kotesovec, Feb 18 2022

Keywords

• nonn

Crossrefs

Cf. A350366, A351507, A351508.

Programs

Mathematica

Table[SeriesCoefficient[Product[(1 + k*x)^n / (1 - k*x)^n, {k,1,n}], {x,0,n}], {n,0,20}]

PARI

a(n) = my(x='x+O(x^(n+1))); polcoef(prod(k=1, n, (1+k*x)^n/ (1-k*x)^n), n); \\ Michel Marcus, Feb 19 2022

Formula

a(n) ~ exp(n + 1) * n^(2*n - 1/2) / sqrt(2*Pi).