A371312 Expansion of e.g.f. Product_{k>=1} 1 / (1 - x^k/k!)^2.

1, 2, 8, 38, 228, 1562, 12386, 109286, 1073988, 11545994, 135393438, 1714890806, 23380747506, 341014477390, 5303722839850, 87582446980418, 1531259993710468, 28254163132485930, 548854481037814382, 11196310379931318758, 239346426732701009838, 5350768890908294837294

Offset: 0

Author

Ilya Gutkovskiy, Mar 24 2024

Keywords

• nonn

Comments

Exponential self-convolution of A005651.

Crossrefs

Cf. A005651, A032312.

Programs

Mathematica

nmax = 21; CoefficientList[Series[Product[1/(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) * A005651(k) * A005651(n-k).

a(n) ~ A247551^2 * n! * n. - Vaclav Kotesovec, Mar 24 2024