A191594 Expansion of (1-exp(x))/(1+x^2-exp(x))=sum(n>=0, a(n)*x^n/n!^2)

1, 1, 2, 3, -48, -1220, -19440, -69720, 14407680, 953539776, 35565868800, -210727440000, -201519805132800, -23287596250913280, -1387143593335019520, 70361372381908608000, 36238719331572645888000, 6110545675513945739673600, 457510061917491552313344000, -86824257027562156263159398400, -44392403385021894430349721600000

Offset

0,3

Links

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

Formula

a(n)=n!^2*sum(m=1..n-1, (m!*sum(k=1..n-m, (k!*stirling1(m+k,m)*stirling2(n-m,k))/(m+k)!))/(n-m)!)+n!^2.

Prog

(Maxima)
a(n):=n!^2*sum((m!*sum((k!*stirling1(m+k, m)*stirling2(n-m, k))/(m+k)!, k, 1, n-m))/(n-m)!, m, 1, n-1)+n!^2;

Crossrefs

Sequence in context: A215536 A173355 A118222 * A208204 A067092 A041133

Adjacent sequences: A191591 A191592 A191593 * A191595 A191596 A191597

Keyword

sign

Author

Vladimir Kruchinin, Jun 07 2011

Status

approved