A384093 a(n) = [x^n] Product_{k=1..n} ((1 + k^2*x)/(1 - k^2*x))^n.

1, 2, 200, 100372, 141369600, 429768373550, 2413602498186776, 22580623631512230760, 326908252720653523943424, 6930499895312478999698799930, 206129722171946147890239366225000, 8311703033335976017330775929889992316, 441845483828200905036741829941273994080000

Offset: 0

Author

Vaclav Kotesovec, May 19 2025

Keywords

• nonn

Crossrefs

Cf. A384091, A384092.

Cf. A351764, A384043.

Programs

Mathematica

Table[SeriesCoefficient[Product[((1+k^2*x)/(1-k^2*x))^n, {k, 1, n}], {x, 0, n}], {n, 0, 15}]

Formula

a(n) ~ 2^(n - 1/2) * exp(n + 3/2) * n^(3*n - 1/2) / (sqrt(Pi) * 3^n).