A383171 Expansion of e.g.f. log(1 + log(1 - 2*x)/2)^2 / 2.

0, 0, 1, 9, 91, 1090, 15298, 247352, 4537132, 93195696, 2120623984, 52973194560, 1441635171040, 42464913775232, 1346297567292416, 45715740985471744, 1655552663185480448, 63698261991541393408, 2595107348458704209920, 111613055867327344582656

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

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

a(n) ~ sqrt(Pi) * log(n) * 2^(n + 1/2) * n^(n - 1/2) / (exp(1) - exp(-1))^n * (1 + (gamma + log(2) - log(exp(2)-1))/log(n)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Apr 18 2025

Prog

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

Crossrefs

Cf. A383170, A383172.

Cf. A341587, A383163.

Sequence in context: A176735 A286786 A123792 * A022520 A020236 A068624

Adjacent sequences: A383168 A383169 A383170 * A383172 A383173 A383174

Keyword

nonn

Author

Seiichi Manyama, Apr 18 2025

Status

approved