A174467 G.f.: exp( Sum_{n>=1} A174468(n)*x^n/n ) where A174468(n) = Sum_{d|n} d*sigma(n/d)*sigma(d).
1, 1, 5, 10, 31, 58, 157, 299, 711, 1367, 2987, 5679, 11807, 22117, 44006, 81513, 156885, 286413, 537058, 967367, 1773882, 3155223, 5677183, 9976095, 17661695, 30682683, 53544796, 92037152, 158575796, 269850363, 459636546, 774851829
Offset: 0
Keywords
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.
Programs
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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)}
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)