A355788 E.g.f. satisfies log(A(x)) = (exp(2*x) - 1) * A(x)/2.
1, 1, 5, 38, 409, 5772, 101227, 2126966, 52153185, 1462998168, 46232500275, 1625693415898, 62972266884721, 2664713395180228, 122315552809623323, 6053803331878334590, 321389617069279569345, 18218906261462603910704, 1098415656103838009681123
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw((1-exp(2*x))/2)))) -
PARI
a(n) = sum(k=0, n, 2^(n-k)*(k+1)^(k-1)*stirling(n, k, 2));
Formula
E.g.f.: exp( -LambertW((1 - exp(2*x))/2) ).
a(n) = Sum_{k=0..n} 2^(n-k) * (k+1)^(k-1) * Stirling2(n,k).
From Vaclav Kotesovec, Jul 18 2022: (Start)
E.g.f.: 2*LambertW((1 - exp(2*x))/2) / (1 - exp(2*x)).
a(n) ~ 2^(n - 1/2) * sqrt(exp(1) + 2) * n^(n-1) / (exp(n-1) * (log(exp(1) + 2) - 1)^(n - 1/2)). (End)