A383166 Expansion of e.g.f. log(1 + (exp(2*x) - 1)/2)^3 / 6.

0, 0, 0, 1, 6, 15, -15, -210, 28, 5292, 4140, -208560, -369864, 11847264, 33630688, -917280000, -3642944640, 92903375616, 479824306944, -11926470604800, -76477342307840, 1892813347934208, 14591875555074048, -363945109924577280, -3293838565260693504, 83374884181664563200

Offset: 0

Author

Seiichi Manyama, Apr 18 2025

Keywords

• sign

Crossrefs

Column k=3 of A209849.

Cf. A383164.

Programs

PARI

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

Formula

a(n) = Sum{k=3..n} 2^(n-k) * Stirling2(n,k) * Stirling1(k,3).