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A330495
a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * (k-1)! * sigma_2(k), where sigma_2 = A001157.
4
1, 6, 37, 307, 2858, 32060, 405830, 5777354, 91400200, 1593023040, 30251766840, 622016655816, 13777150847952, 327040289212320, 8280040187137200, 222696435041359824, 6341359225470493440, 190609840724078576256, 6031297367477133540480, 200389374367707186619776
OFFSET
1,2
LINKS
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