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%I #22 Jun 20 2023 11:30:17
%S 0,1,-1,2,-10,46,-226,1532,-11880,96136,-882376,9179312,-102310000,
%T 1223945776,-15941391376,222827194592,-3303846357120,52077034777216,
%U -871329939918976,15375474411183872,-285315305595562240,5562663216718387456,-113653337185088018176
%N Expansion of e.g.f.: tan(log(1+tanh(x))).
%F a(n)=sum(m=0..(n-1)/2, (sum(j=1..2*m+1, j!*2^(2*m-j+1)*(-1)^(m+j+1)* stirling2(2*m+1,j)))*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!)). - _Vladimir Kruchinin_, Jun 21 2011
%F a(n) ~ (-1)^(n+1) * n! / ((2-exp(-Pi/2)) * (log(2*exp(Pi/2)-1)/2)^(n+1)). - _Vaclav Kotesovec_, Feb 02 2015
%t CoefficientList[Series[Tan[Log[1+Tanh[x]]], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Feb 02 2015 *)
%o (Maxima)
%o a(n):=sum((sum(j!*2^(2*m-j+1)*(-1)^(m+j+1)*stirling2(2*m+1,j),j,1,2*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),m,0,(n-1)/2); /* _Vladimir Kruchinin_ Jun 21 2011 */
%K sign,easy
%O 0,4
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
%E Definition clarified by _Harvey P. Dale_, Jun 20 2023
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