OFFSET
0,4
FORMULA
a(n)=sum(m=1..n, sum(i=0..n-m, binomial(n,i+m)*(m^(n-i-m)*(sum(k=0..i+m, stirling2(i+m,k+m)*2^(i-k)*binomial(k+m-1,m-1)*(k+m)!*(-1)^(k+n-i-m)))))/m!), n>0, a(0)=1. - Vladimir Kruchinin, Jun 06 2011
MATHEMATICA
Exp[ Tanh[ x ]/Exp[ x ] ]
CoefficientList[Series[E^(Tanh[x]/E^x), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)
PROG
(Maxima)
a(n):=sum(sum(binomial(n, i+m)*(m^(n-i-m)*(sum(stirling2(i+m, k+m)*2^(i-k)*binomial(k+m-1, m-1)*(k+m)!*(-1)^(k+n-i-m), k, 0, i+m))), i, 0, n-m)/m!, m, 1, n); /* Vladimir Kruchinin, Jun 06 2011 */
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
STATUS
approved