OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..400
FORMULA
E.g.f.: Sum_{k>=1} log(1/(1 - x))^k / (k * (1 - log(1/(1 - x))^k)^2).
a(n) ~ n! * zeta(3) * n * exp(n) / (exp(1) - 1)^(n+2).
MATHEMATICA
Table[Sum[(-1)^(n-k) * StirlingS1[n, k] * (k-1)! * DivisorSigma[2, k], {k, 1, n}], {n, 1, 20}]
nmax = 20; Rest[CoefficientList[Series[Sum[Log[1/(1 - x)]^k/(k*(1 - Log[1/(1 - x)]^k)^2), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!]
PROG
(PARI) a(n) = sum(k=1, n, (-1)^(n-k)*stirling(n, k, 1)*(k-1)!*sigma(k, 2)); \\ Michel Marcus, Dec 16 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Dec 16 2019
STATUS
approved