OFFSET
0,3
LINKS
Lida Ahmadi, Ricardo Gómez Aíza, and Mark Daniel Ward, A unified treatment of families of partition functions, La Matematica (2024). Preprint available as arXiv:2303.02240 [math.CO], 2023.
FORMULA
From Ricardo Gómez Aíza, Mar 08 2023: (Start)
E.g.f.: Product_{n>=1,m>=1,k>=1} 1 / (1 - x^(n * m * k))^n.
log(a(n) / n!) ~ (3/2) * (Zeta(3) * Pi^4 / 18)^(1/3) * n^(2/3). (End)
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, x^m/m*sumdiv(m, d, d*sigma(m/d)*sigma(d)))+x*O(x^n)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 04 2010
STATUS
approved