A009311 - OEIS

%I #17 Apr 01 2017 14:01:24

%S 0,1,-2,5,-19,104,-706,5662,-53082,570600,-6897016,92565296,

%T -1366706848,22016867248,-384226243584,7220865546000,-145397565641296,

%U 3122890640031488,-71266398589322368,1722010388581604224

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

%F a(n)=sum(m=1..n, ((-1)^(m-1)*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!))/m). - _Vladimir Kruchinin_, Jun 21 2011

%F a(n) ~ (n-1)! * (-1)^(n+1) * 2^n / (log(2*exp(1)-1))^n. - _Vaclav Kotesovec_, Jan 22 2015

%t CoefficientList[Series[Log[1 + Log[1 + Tanh[x]]], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 22 2015 *)

%o (Maxima)

%o a(n):=sum(((-1)^(m-1)*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,m,1,n); /* _Vladimir Kruchinin_, Jun 21 2011 */

%K sign,easy

%O 0,3

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997