A371546 Expansion of e.g.f. Product_{k>=1} 1 / (1 - 2*x^k/k!).
1, 2, 10, 62, 522, 5262, 64006, 897990, 14416618, 259650638, 5197438710, 114360488310, 2745242514966, 71378953200310, 1998718342001062, 59962112293963182, 1918813454880552298, 65239810516299767310, 2348641102002493520086, 89248414267689180772278, 3569939582019832830181222
Offset: 0
Keywords
Programs
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Mathematica
nmax = 20; CoefficientList[Series[Product[1/(1 - 2 x^k/k!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Formula
a(n) ~ c * 2^n * n!, where c = Product_{k>=2} 1/(1 - 2^(1-k)/k!) = 1.39938283723373672673056837661175942499559257652969647531100283042201554... - Vaclav Kotesovec, Mar 28 2024