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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 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A330449, A330450, A330493, A330494. Sequence in context: A300171 A218298 A179515 * A288703 A337552 A036358 Adjacent sequences: A330492 A330493 A330494 * A330496 A330497 A330498 KEYWORD nonn AUTHOR Vaclav Kotesovec, Dec 16 2019 STATUS approved

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Last modified September 13 22:05 EDT 2024. Contains 375910 sequences. (Running on oeis4.)