OFFSET
0,3
LINKS
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
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Apr 21 2011
EXTENSIONS
Definition clarified by Harvey P. Dale, Mar 29 2020
STATUS
approved