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%I #28 Mar 24 2024 08:19:59
%S 1,2,8,40,254,1868,15996,153144,1637520,19191072,245463936,3390905472,
%T 50406479328,800678811840,13547088596544,242995426574976,
%U 4607744279916672,92046384885051648,1932579234508861440,42530614791735573504,979132781170084872960,23529915213836747927040
%N Expansion of e.g.f. Product_{k>=1} 1 / (1 - x^k/k)^2.
%C Exponential self-convolution of A007841.
%F a(n) = Sum_{k=0..n} binomial(n,k) * A007841(k) * A007841(n-k).
%F a(n) ~ exp(-2*gamma) * n! * n^3 / 6, where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Mar 24 2024
%t nmax = 21; CoefficientList[Series[Product[1/(1 - x^k/k)^2, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A007841, A371312, A371389.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Mar 24 2024