A191577 - OEIS

%I #6 Mar 31 2012 10:23:14

%S 1,3,12,54,228,540,-3840,-50400,229824,11430720,-10886400,-5388768000,

%T -24417676800,4733158510080,58758168268800,-7139902049280000,

%U -165279578720256000,17368039270213632000,645434329747208601600,-64796782524129976320000,-3555479864273411063808000

%N Expansion of (x*exp(x)/(exp(x)-1))^3 = sum(n>=0, a(n)/(n!*(n+1)!)*x^n)

%F 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.

%F 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!)

%o (Maxima)

%o a(n):=6*(-1)^n*sum((stirling1(k+3,3)*stirling2(n,k))/((k+1)*(k+2)*(k+3)),k,1,n);

%K sign

%O 0,2

%A _Vladimir Kruchinin_, Jun 07 2011