A168468 - OEIS

%I #11 Nov 21 2013 12:49:44

%S 1,0,1,-3,8,-40,256,-1568,11108,-96720,908836,-9084108,101147408,

%T -1233325600,15998088016,-221845635248,3301710539408,-52192183735680,

%U 871157943761296,-15360373687021488,285403775884452608

%N E.g.f. sec(log(1+tanh(x)))

%F a(n)=2*sum(m=1..n/2, (sum(j=0..m, binomial(2*j,j)*4^(m-2*j)*sum(i=0..j, (i-j)^(2*m)* binomial(2*j,i)*(-1)^(m+j-i))))*sum(r=2*m..n, (stirling1(r,2*m)*sum(k=r..n, binomial(k-1,r-1)*k!*2^(n-k)*stirling2(n,k)*(-1)^(r+k)))/r!)), n>0, a(0)=1.

%t With[{nn=20},CoefficientList[Series[Sec[Log[1+Tanh[x]]],{x,0,nn}], x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 06 2011 *)

%o (Maxima)

%o a(n):=if n=0 then 1 else 2*sum((sum(binomial(2*j,j)*4^(m-2*j)*sum((i-j)^(2*m)*binomial(2*j,i)*(-1)^(m+j-i),i,0,j),j,0,m))*sum((stirling1(r,2*m)*sum(binomial(k-1,r-1)*k!*2^(n-k)*stirling2(n,k)*(-1)^(r+k),k,r,n))/r!,r,2*m,n),m,1,n/2);

%K sign

%O 0,4

%A _Vladimir Kruchinin_, Jun 21 2011