A367423 Expansion of e.g.f. 1 / sqrt(1 + log(1 - 2*x)).
1, 1, 5, 41, 465, 6729, 118437, 2455809, 58630401, 1584058161, 47783202213, 1591924168185, 58055219617425, 2300356943749305, 98409722434170885, 4520749198158270225, 221954573405993807745, 11598560660172502840545, 642753897983638032821445
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, 2^(n-k)*prod(j=0, k-1, 2*j+1)*abs(stirling(n, k, 1)));
Formula
a(n) = Sum_{k=0..n} 2^(n-k) * (Product_{j=0..k-1} (2*j+1)) * |Stirling1(n,k)|.
a(0) = 1; a(n) = Sum_{k=1..n} 2^k * (1 - 1/2 * k/n) * (k-1)! * binomial(n,k) * a(n-k).
a(n) ~ 2^(n + 1/2) * n^n / (exp(1) - 1)^(n + 1/2). - Vaclav Kotesovec, Jun 09 2025