A384043 a(n) = [x^n] Product_{k=1..n} (1 + k^2*x) / (1 - k^2*x).

1, 2, 50, 4188, 735600, 221302710, 101667388082, 66218673102680, 58048466179356672, 65901249246347377770, 94061755750395244537250, 164863945136411230998746612, 348110204753572939058548570000, 871547135491620353615820806025918, 2552918049709989779004770502542335650

Offset: 0

Author

Vaclav Kotesovec, May 18 2025

Keywords

• nonn

Crossrefs

Cf. A001044, A298851.

Cf. A350366, A384044, A351764.

Programs

Mathematica

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

Formula

a(n) ~ c * d^n * n!^2 / n^(3/2), where d = 16.6871576653578743696262746377576281620174969944584774545888... and c = 0.1371163625236187865398447973928851799479072107076663329994...