A330493 a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * (k-1)! * tau(k), where tau = A000005.

1, 3, 12, 70, 492, 4298, 43894, 514666, 6830888, 101473632, 1664125944, 29858266392, 582481147440, 12281821373040, 278257595964576, 6739505703156192, 173785740554811264, 4754455742416944000, 137571331202872821504, 4197696814883284962048

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

Cf. A330351, A330352, A330494, A330495.

Sequence in context: A077460 A001205 A346888 * A112320 A103366 A335643

Adjacent sequences: A330490 A330491 A330492 * A330494 A330495 A330496

Keyword

nonn

Author

Vaclav Kotesovec, Dec 16 2019

Status

approved