A191368 Expansion of (x*exp(x)/(exp(x)-1))^2 = sum(n>=0, a(n)/(n!*(n+1)!)*x^n).

1, 2, 5, 12, 12, -120, -600, 6720, 84672, -1088640, -27216000, 399168000, 17337576960, -286858091520, -19833061248000, 366148823040000, 37838865512448000, -771912856453939200, -113678565831806976000, 2541050295063920640000, 513635665355584192512000

Offset

0,2

Comments

(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!).

Links

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

Formula

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.

Prog

(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);

Crossrefs

Sequence in context: A125199 A103832 A348891 * A085227 A324601 A305310

Adjacent sequences: A191365 A191366 A191367 * A191369 A191370 A191371

Keyword

sign

Author

Vladimir Kruchinin, Jun 07 2011

Status

approved