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A009198
E.g.f. exp(log(1+x)/exp(x)).
3
1, 1, -2, 0, 18, -85, 155, 1057, -13636, 86361, -271783, -1518539, 35743378, -376883351, 2663534939, -8383983593, -117620643336, 2907896789457, -39364767602331, 389671721253889, -2504052803057234, -3842812946739679, 465976686530941599
OFFSET
0,3
COMMENTS
For n>=40 the +- signs alternate regularly. - Vaclav Kotesovec, May 13 2022
LINKS
FORMULA
a(n)=sum(k=1..n, sum(i=k..n, binomial(n,i)*(stirling1(i,k)*k^(n-i)*(-1)^(n-i)))), n > 0, a(0)=1. - Vladimir Kruchinin, Jun 29 2011
a(n) ~ n! * (-1)^n / (Gamma(-exp(1)) * n^(1+exp(1))) * (1 - (exp(2) + exp(1)) * log(n)/n). - Vaclav Kotesovec, May 13 2022
MATHEMATICA
nmax = 20; CoefficientList[Series[E^(Log[1+x]/E^x), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, May 13 2022 *)
PROG
(Maxima)
a(n):=if n=0 then 1 else sum(sum(binomial(n, i)*(stirling1(i, k)*k^(n-i)*(-1)^(n-i)), i, k, n), k, 1, n); /* Vladimir Kruchinin, Jun 29 2011 */
CROSSREFS
Sequence in context: A349036 A361591 A261516 * A209123 A139003 A264881
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
STATUS
approved