The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A327601 Expansion of e.g.f. exp(x) * Product_{k>=1} 1/(1 - (1 - exp(x))^k). 2
 1, 0, 2, 0, 26, 120, 1922, 21840, 307946, 4251240, 63165842, 1010729280, 18501318266, 391496665560, 9265945721762, 232411950454320, 5972325812958986, 156131611764907080, 4208451299935189682, 119669466221148348960, 3658459009408581118106 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Stirling-Bernoulli transform of partition numbers (A000041). LINKS FORMULA a(n) = Sum_{k=0..n} (-1)^k * Stirling2(n+1,k+1) * k! * A000041(k). MATHEMATICA nmax = 20; CoefficientList[Series[Exp[x] Product[1/(1 - (1 - Exp[x])^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! Table[Sum[(-1)^k StirlingS2[n + 1, k + 1] k! PartitionsP[k], {k, 0, n}], {n, 0, 20}] PROG (PARI) a(n) = sum(k=0, n, (-1)^k*stirling(n+1, k+1, 2)*k!*numbpart(k)); \\ Michel Marcus, Sep 19 2019 CROSSREFS Cf. A000041, A167137, A306022, A306042. Sequence in context: A157304 A157305 A306416 * A336287 A337074 A156459 Adjacent sequences: A327598 A327599 A327600 * A327602 A327603 A327604 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Sep 18 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 27 18:31 EDT 2023. Contains 361575 sequences. (Running on oeis4.)