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%I #8 Mar 27 2019 10:04:23
%S 0,1,1,-1,-11,-33,61,1367,7253,-12561,-580499,-4701497,4669765,
%T 580325215,6636339165,1365901495,-1122870368715,-17289945450289,
%U -31110588453299,3713822629274023,74717183313957413,280555705771423039,-19253195126787261507,-496715617694137066089,-3008746115751273626347
%N Expansion of e.g.f. tanh(exp(x)-1).
%F E.g.f.: sinh(exp(x)-1)/cosh(exp(x)-1).
%F E.g.f.: (exp(x)-1)/(1 + (exp(x)-1)^2/(3 + (exp(x)-1)^2/(5 + (exp(x)-1)^2/(7 + (exp(x)-1)^2/(9 + ...))))), a continued fraction.
%e tanh(exp(x)-1) = x/1! + x^2/2! - x^3/3! - 11*x^4/4! - 33*x^5/5! + 61*x^6/6! + 1367*x^7/7! + ...
%p a:=series(tanh(exp(x)-1),x=0,25): seq(n!*coeff(a,x,n),n=0..24); # _Paolo P. Lava_, Mar 27 2019
%t nmax = 24; CoefficientList[Series[Tanh[Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 24; CoefficientList[Series[Sinh[Exp[x] - 1]/Cosh[Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 24; CoefficientList[Series[(Exp[x] - 1)/(1 + ContinuedFractionK[(Exp[x] - 1)^2, 2 k - 1, {k, 2, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A009752, A024429, A024430, A080832, A296544.
%K sign
%O 0,5
%A _Ilya Gutkovskiy_, Dec 15 2017
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