A383163 Expansion of e.g.f. log(1 - (exp(2*x) - 1)/2)^2 / 2.

0, 0, 1, 9, 75, 690, 7290, 88536, 1223628, 19019664, 328908720, 6268688448, 130615236576, 2954657491968, 72128519473920, 1890266313945600, 52937770062975744, 1577901064699594752, 49877742373556336640, 1666688195869095124992, 58704547943954039672832

Offset

0,4

Links

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

Formula

a(n) = Sum{k=2..n} 2^(n-k) * Stirling2(n,k) * |Stirling1(k,2)|.

a(n) ~ sqrt(Pi) * 2^(n + 1/2) * n^(n - 1/2) * log(n) / (exp(n) * log(3)^n). - Vaclav Kotesovec, Apr 18 2025

Prog

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

Crossrefs

Column k=2 of A383149.

Cf. A000254.

Sequence in context: A351513 A136659 A231592 * A335345 A126965 A066222

Adjacent sequences: A383160 A383161 A383162 * A383164 A383165 A383166

Keyword

nonn

Author

Seiichi Manyama, Apr 18 2025

Status

approved