OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..400
FORMULA
E.g.f.: -Sum_{k>=1} log(1 - log(1/(1 - x))^k) / k.
a(n) ~ n! * (log(n) + 2*gamma - log(exp(1) - 1)) / (n * (1 - exp(-1))^n), where gamma is the Euler-Mascheroni constant A001620.
MATHEMATICA
Table[Sum[(-1)^(n-k) * StirlingS1[n, k] * (k-1)! * DivisorSigma[0, k], {k, 1, n}], {n, 1, 20}]
nmax = 20; Rest[CoefficientList[Series[-Sum[Log[1 - Log[1/(1 - x)]^k]/k, {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)!*numdiv(k)); \\ Michel Marcus, Dec 16 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Dec 16 2019
STATUS
approved