OFFSET
0,4
FORMULA
a(n)=sum(m=0..(n-1)/2, ((-1)^(m)*(2*m+1)!*sum(r=2*m+1..n, (stirling1(r,2*m+1)*sum(k=r..n, binomial(k-1,r-1)*k!*2^(n-k)*stirling2(n,k)*(-1)^(r+k)))/r!))/(2*m+1)), n>0.
MATHEMATICA
With[{nn=30}, CoefficientList[Series[ArcTan[Log[1+Tanh[x]]], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Jan 03 2013 *)
PROG
(Maxima)
a(n):=sum(((-1)^(m)*(2*m+1)!*sum((stirling1(r, 2*m+1)*sum(binomial(k-1, r-1)*k!*2^(n-k)*stirling2(n, k)*(-1)^(r+k), k, r, n))/r!, r, 2*m+1, n))/(2*m+1), m, 0, (n-1)/2);
CROSSREFS
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Jun 21 2011
STATUS
approved