A191577 Expansion of (x*exp(x)/(exp(x)-1))^3 = sum(n>=0, a(n)/(n!*(n+1)!)*x^n)

1, 3, 12, 54, 228, 540, -3840, -50400, 229824, 11430720, -10886400, -5388768000, -24417676800, 4733158510080, 58758168268800, -7139902049280000, -165279578720256000, 17368039270213632000, 645434329747208601600, -64796782524129976320000, -3555479864273411063808000

Offset

0,2

Links

Table of n, a(n) for n=0..20.

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

Sequence in context: A124810 A370821 A329056 * A282901 A123348 A151204

Adjacent sequences: A191574 A191575 A191576 * A191578 A191579 A191580

Keyword

sign

Author

Vladimir Kruchinin, Jun 07 2011

Status

approved