|
%I #15 Sep 06 2020 16:42:43
%S 1,1,1,0,-4,-10,14,196,440,-3168,-27856,-16192,1164272,7585552,
%T -23621872,-695464800,-3191206912,38919085184,661218763136,
%U 1320994868224,-74958266666752,-932434904045568,2633042904931328,193750955482836992
%N Expansion of e.g.f.: 1/(1-log(1+tanh(x)))
%F a(n)=sum(m=1..n, m!*sum(r=m..n, (stirling1(r,m)*sum(k=r..n, binomial(k-1,r-1)*k!*2^(n-k)*stirling2(n,k)*(-1)^(r+k)))/r!)), n>0, n(0)=1.
%t With[{nn=30},CoefficientList[Series[1/(1-Log[1+Tanh[x]]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Sep 06 2020 *)
%o (Maxima)
%o a(n):=sum(m!*sum((stirling1(r,m)*sum(binomial(k-1,r-1)*k!*2^(n-k)*stirling2(n,k)*(-1)^(r+k),k,r,n))/r!,r,m,n),m,1,n);
%K sign
%O 0,5
%A _Vladimir Kruchinin_, Jun 20 2011
%E Definition clarified by _Harvey P. Dale_, Sep 06 2020
|
