A141003 Expansion of e.g.f. exp(Sum_{d|M} (exp(d*x)-1)/d), M=4.

1, 3, 16, 111, 931, 9066, 99925, 1224579, 16466524, 240481659, 3783550243, 63705870894, 1141642250521, 21673475232051, 434151377912680, 9144596750676663, 201921333704487283, 4661560653703827474, 112247618536314408013, 2813147392487637246483

Offset: 0

Author

R. J. Mathar, Jul 11 2008

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• J. Pasukonis, S. Ramgoolam, From counting to construction for BPS states in N=4 SYM, arXiv:1010.1683 [hep-th], 2010, (E.4).
• J. Pasukonis, S. Ramgoolam, From counting to construction for BPS states in N=4 SYM, J. High En. Phys. 2011 (2) (2011), (E.4).

Crossrefs

Column 4 of A162663. u[n,j] generates the j-th column of A162663. - Wouter Meeussen, Dec 06 2008; Danny Rorabaugh, Oct 29 2015

Programs

Mathematica

u[0,j_]:=1;u[k_,j_]:=u[k,j]=Sum[Binomial[k-1,i-1]Plus@@(u[k-i,j]#^(i-1)&/@Divisors[j]),{i,k}]; Table[u[n,4],{n,0,12}] (* Wouter Meeussen, Dec 06 2008 *)