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%I #7 Mar 30 2024 02:33:34
%S 1,2,10,62,522,5262,64006,897990,14416618,259650638,5197438710,
%T 114360488310,2745242514966,71378953200310,1998718342001062,
%U 59962112293963182,1918813454880552298,65239810516299767310,2348641102002493520086,89248414267689180772278,3569939582019832830181222
%N Expansion of e.g.f. Product_{k>=1} 1 / (1 - 2*x^k/k!).
%F a(n) ~ c * 2^n * n!, where c = Product_{k>=2} 1/(1 - 2^(1-k)/k!) = 1.39938283723373672673056837661175942499559257652969647531100283042201554... - _Vaclav Kotesovec_, Mar 28 2024
%t nmax = 20; CoefficientList[Series[Product[1/(1 - 2 x^k/k!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A005651, A032297, A070933.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Mar 27 2024