OFFSET
0,6
FORMULA
G.f. (x/(exp(x)-1))^x
a(n):=sum(m=1..n, (-1)^m*sum(k-m..n-m, (stirling1(k,m)*sum(j=1..k, ((-1)^(j-k)*stirling2(n-m+j,j))/((k-j)!*(n-m+j)!))))), a(0)=1.
EXAMPLE
A(x)=1- x^2/2 - x^3/24 + x^4/8 + 61*x^5/2880 - 23*x^6/1152 - 391*x^7/72576 + 149*x^8/69120 + 8731*x^9/9676800 - 50299*x^10/348364800 + ...
PROG
(Maxima)
a(n):=if n=0 then 1 else sum((-1)^m*sum((stirling1(k, m)*sum(((-1)^(j-k)*stirling2(n-m+j, j))/((k-j)!*(n-m+j)!), j, 1, k)), k, m, n-m), m, 1, n);
CROSSREFS
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Nov 09 2011
STATUS
approved