A366751 Expansion of e.g.f. -log(1 - x^3 * (exp(x) - 1)).

0, 0, 0, 0, 24, 60, 120, 210, 20496, 181944, 1059120, 4990590, 180292200, 3191349876, 36598884504, 327837512730, 7732754793120, 194896185648240, 3574721299186656, 51311061420097014, 1105883184455171640, 32127696556638165420, 812811279492629700360

Offset

0,5

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = n! * Sum_{k=1..floor(n/4)} (k-1)! * Stirling2(n-3*k,k)/(n-3*k)!.

Mathematica

With[{nn=30}, CoefficientList[Series[-Log[1-x^3 (Exp[x]-1)], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 22 2026 *)

Prog

(PARI) a(n) = n!*sum(k=1, n\4, (k-1)!*stirling(n-3*k, k, 2)/(n-3*k)!);

Crossrefs

Cf. A052858, A366564.

Cf. A368174.

Sequence in context: A163636 A279930 A292891 * A358014 A356950 A392897

Adjacent sequences: A366748 A366749 A366750 * A366752 A366753 A366754

Keyword

nonn

Author

Seiichi Manyama, Dec 15 2023

Status

approved