The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A330493 a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * (k-1)! * tau(k), where tau = A000005. 5
 1, 3, 12, 70, 492, 4298, 43894, 514666, 6830888, 101473632, 1664125944, 29858266392, 582481147440, 12281821373040, 278257595964576, 6739505703156192, 173785740554811264, 4754455742416944000, 137571331202872821504, 4197696814883284962048 (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 - 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: A125862 A077460 A001205 * A112320 A103366 A277457 Adjacent sequences:  A330490 A330491 A330492 * A330494 A330495 A330496 KEYWORD nonn AUTHOR Vaclav Kotesovec, Dec 16 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 29 14:37 EDT 2020. Contains 333107 sequences. (Running on oeis4.)