A371313 Expansion of e.g.f. Product_{k>=1} 1 / (1 - x^k/k)^2.

1, 2, 8, 40, 254, 1868, 15996, 153144, 1637520, 19191072, 245463936, 3390905472, 50406479328, 800678811840, 13547088596544, 242995426574976, 4607744279916672, 92046384885051648, 1932579234508861440, 42530614791735573504, 979132781170084872960, 23529915213836747927040

Offset

0,2

Comments

Exponential self-convolution of A007841.

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A007841(k) * A007841(n-k).

a(n) ~ exp(-2*gamma) * n! * n^3 / 6, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Mar 24 2024

Mathematica

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

Crossrefs

Cf. A007841, A371312, A371389.

Sequence in context: A349105 A259869 A321733 * A000828 A296676 A281910

Adjacent sequences: A371310 A371311 A371312 * A371314 A371315 A371316

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 24 2024

Status

approved