A371389 Expansion of e.g.f. Product_{k>=1} (1 + x^k/k)^2.

1, 2, 4, 16, 74, 388, 2756, 20872, 180008, 1758672, 18937152, 221914944, 2832193008, 39039810912, 575502635808, 9100950684480, 152818028328960, 2717564023296000, 51129136369981440, 1012979833297735680, 21074454817487953920, 460035753479203184640

Offset: 0

Author

Ilya Gutkovskiy, Mar 24 2024

Keywords

• nonn

Comments

Exponential self-convolution of A007838.

Crossrefs

Cf. A007838, A032312, A371313.

Programs

Mathematica

nmax = 21; CoefficientList[Series[Product[(1 + x^k/k)^2, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A007838(k) * A007838(n-k).

a(n) ~ exp(-2*gamma) * n! * n, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Mar 24 2024