|
%I #23 Mar 31 2012 10:23:14
%S 1,2,5,12,12,-120,-600,6720,84672,-1088640,-27216000,399168000,
%T 17337576960,-286858091520,-19833061248000,366148823040000,
%U 37838865512448000,-771912856453939200,-113678565831806976000,2541050295063920640000,513635665355584192512000
%N Expansion of (x*exp(x)/(exp(x)-1))^2 = sum(n>=0, a(n)/(n!*(n+1)!)*x^n).
%C (x*exp(x)/(exp(x)-1))^m = 1+sum(n>0, ((-1)^n*sum(k=1..n, (stirling1(m+k,m) *stirling2(n,k))/binomial(m+k,k)))*x^n/n!).
%F a(n) = 2*(-1)^n*(n+1)!*sum(k=1..n, (stirling1(k+2,2) *stirling2(n,k))/((k+1)*(k+2))), a(0)=1.
%o (Maxima) a(n):=if(n=0 then 1 else 2*(-1)^n*(n+1)!* sum((stirling1(k+2,2) *stirling2(n, k))/((k+1)*(k+2)), k, 1, n);
%K sign
%O 0,2
%A _Vladimir Kruchinin_, Jun 07 2011
|
