OFFSET
0,2
FORMULA
a(n)=6*(-1)^n*sum(k=1..n, (stirling1(k+3,3)*stirling2(n,k))/((k+1)*(k+2)*(k+3))), a(n)>0, a(0)=1.
The above is the special case m=3 of (x*exp(x)/(exp(x)-1))^m = 1+sum(n>=1, ((-1)^n*sum(k=1..n, (stirling1(m+k,m)*stirling2(n,k))/binomial(m+k,k)))*x^n/n!)
PROG
(Maxima)
a(n):=6*(-1)^n*sum((stirling1(k+3, 3)*stirling2(n, k))/((k+1)*(k+2)*(k+3)), k, 1, n);
CROSSREFS
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Jun 07 2011
STATUS
approved