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

0,5

Links

Table of n, a(n) for n=0..20.

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

Prog

(PARI) a(n) = sum(k=3, n, 2^(n-k)*stirling(n, k, 2)*abs(stirling(k, 3, 1)));

Crossrefs

Column k=3 of A383149.

Cf. A000399, A383166.

Sequence in context: A157708 A159537 A136660 * A374880 A374862 A362808

Adjacent sequences: A383161 A383162 A383163 * A383165 A383166 A383167

Keyword

nonn

Author

Seiichi Manyama, Apr 18 2025

Status

approved