A383170 Expansion of e.g.f. -log(1 + log(1 - 2*x)/2).
0, 1, 3, 16, 122, 1208, 14704, 212336, 3547984, 67337728, 1430990976, 33664165632, 868592478720, 24390846882816, 740570519159808, 24177326011834368, 844599686386919424, 31438092340685144064, 1242230898248798896128, 51933512200489564962816, 2290351520336982559358976
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=1, n, 2^(n-k)*abs(stirling(n, k, 1)*stirling(k, 1, 1)));
Formula
a(n) = Sum_{k=1..n} 2^(n-k) * |Stirling1(n,k) * Stirling1(k,1)|.
a(n) ~ sqrt(Pi) * 2^(n + 1/2) * n^(n - 1/2) / (exp(1) - exp(-1))^n. - Vaclav Kotesovec, Apr 18 2025