A383164 Expansion of e.g.f. -log(1 - (exp(2*x) - 1)/2)^3 / 6.
0, 0, 0, 1, 18, 255, 3555, 52290, 831684, 14405580, 271688580, 5562400800, 123123764808, 2933953637472, 74953425290016, 2044855241694720, 59361121229581440, 1827578437315965696, 59494057195888597248, 2042194772007257103360, 73731225467600254686720
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=3, n, 2^(n-k)*stirling(n, k, 2)*abs(stirling(k, 3, 1)));
Formula
a(n) = Sum{k=3..n} 2^(n-k) * Stirling2(n,k) * |Stirling1(k,3)|.
a(n) ~ sqrt(Pi) * 2^(n - 1/2) * n^(n - 1/2) * log(n)^2 / (exp(n) * log(3)^n). - Vaclav Kotesovec, Apr 18 2025