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

0,3

Links

Table of n, a(n) for n=0..31.

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

Cf. A174465, A000203 (sigma).

Sequence in context: A032296 A052648 A020995 * A005201 A221304 A094234

Adjacent sequences: A174464 A174465 A174466 * A174468 A174469 A174470

Keyword

nonn

Author

Paul D. Hanna, Apr 04 2010

Status

approved