A189425 Expansion of e.g.f.: exp(log(1+x)-log(1+x)^2)

1, 1, -2, 0, 14, -70, 232, -308, -4044, 58788, -574392, 4926768, -38678088, 265429320, -1203040512, -6939932400, 339735301008, -7509538816752, 140461600744032, -2473675024255104, 42534077510399712

Offset

0,3

Links

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

Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

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: A088504 A229091 A369243 * 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