A330494 a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * (k-1)! * sigma(k), where sigma = A000203.

1, 4, 19, 129, 1018, 9912, 111074, 1416398, 20295208, 323437728, 5657339928, 107765338920, 2223272444976, 49399021063584, 1175549092374672, 29822113966614768, 803485297880792064, 22917198585269729664, 689927737384840662144, 21861972842959846530432

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)).

a(n) ~ n! * Pi^2 * exp(n) / (6 * (exp(1) - 1)^(n+1)).

Mathematica

Table[Sum[(-1)^(n-k) * StirlingS1[n, k] * (k-1)! * DivisorSigma[1, 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)), {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)); \\ Michel Marcus, Dec 16 2019

Crossrefs

Cf. A330353, A330354, A330493, A330495.

Sequence in context: A330515 A330534 A366182 * A352306 A352327 A305867

Adjacent sequences: A330491 A330492 A330493 * A330495 A330496 A330497

Keyword

nonn

Author

Vaclav Kotesovec, Dec 16 2019

Status

approved