A191564 Expansion of exp(x*Bernoulli(x)) = 1+sum(n>0, a(n)/(n!)^2*x^n)

1, 1, 0, -9, 0, 700, -1800, -188160, 2069760, 114198336, -3503606400, -114527952000, 9096958886400, 105465242488320, -34233337027169280, 553613206386240000, 171717284043841536000, -10454299523104595558400

Offset

0,4

Links

Table of n, a(n) for n=0..17.

Formula

a(n)=n!+(n!)^2*(sum(m=1..n-1, sum(k=1..n-m, (k!*stirling1(m+k,m)*stirling2(n-m,k))/(m+k)!)/(n-m)!)), n>0, a(0)=1.

Prog

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

Crossrefs

Sequence in context: A177145 A178912 A380564 * A067479 A308803 A249489

Adjacent sequences: A191561 A191562 A191563 * A191565 A191566 A191567

Keyword

sign

Author

Vladimir Kruchinin, Jun 06 2011

Status

approved