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%I #41 Mar 24 2024 08:21:02
%S 1,2,4,16,74,388,2756,20872,180008,1758672,18937152,221914944,
%T 2832193008,39039810912,575502635808,9100950684480,152818028328960,
%U 2717564023296000,51129136369981440,1012979833297735680,21074454817487953920,460035753479203184640
%N Expansion of e.g.f. Product_{k>=1} (1 + x^k/k)^2.
%C Exponential self-convolution of A007838.
%F a(n) = Sum_{k=0..n} binomial(n,k) * A007838(k) * A007838(n-k).
%F a(n) ~ exp(-2*gamma) * n! * n, where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Mar 24 2024
%t nmax = 21; CoefficientList[Series[Product[(1 + x^k/k)^2, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A007838, A032312, A371313.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Mar 24 2024