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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

Table of n, a(n) for n=0..20.

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

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Last modified October 22 11:53 EDT 2021. Contains 348168 sequences. (Running on oeis4.)