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A189425 Expansion of e.g.f.: exp(log(1+x)-log(1+x)^2) 0
1, 1, -2, 0, 14, -70, 232, -308, -4044, 58788, -574392, 4926768, -38678088, 265429320, -1203040512, -6939932400, 339735301008, -7509538816752, 140461600744032, -2473675024255104, 42534077510399712 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582

FORMULA

a(n)=sum(m=1..n, sum(k=m..n, k!*binomial(m,k-m)*(-1)^(k-m)*stirling1(n,k))/m!), n>0, a(0)=1.

MATHEMATICA

With[{nn=20}, CoefficientList[Series[Exp[Log[1+x]-Log[1+x]^2], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 29 2020 *)

PROG

(Maxima)

a(n):=sum(sum(k!*binomial(m, k-m)*(-1)^(k-m)*stirling1(n, k), k, m, n)/m!, m, 1, n);

CROSSREFS

Sequence in context: A064855 A088504 A229091 * A266169 A277928 A232423

Adjacent sequences:  A189422 A189423 A189424 * A189426 A189427 A189428

KEYWORD

sign

AUTHOR

Vladimir Kruchinin, Apr 21 2011

EXTENSIONS

Definition clarified by Harvey P. Dale, Mar 29 2020

STATUS

approved

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Last modified February 25 19:39 EST 2021. Contains 341618 sequences. (Running on oeis4.)