A296543 Expansion of e.g.f. tanh(exp(x)-1).

0, 1, 1, -1, -11, -33, 61, 1367, 7253, -12561, -580499, -4701497, 4669765, 580325215, 6636339165, 1365901495, -1122870368715, -17289945450289, -31110588453299, 3713822629274023, 74717183313957413, 280555705771423039, -19253195126787261507, -496715617694137066089, -3008746115751273626347

Offset: 0

Author

Ilya Gutkovskiy, Dec 15 2017

Keywords

• sign

Examples

			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! + ...
		

Crossrefs

Cf. A009752, A024429, A024430, A080832, A296544.

Programs

Maple

a:=series(tanh(exp(x)-1),x=0,25): seq(n!*coeff(a,x,n),n=0..24); # Paolo P. Lava, Mar 27 2019

Mathematica

nmax = 24; CoefficientList[Series[Tanh[Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 24; CoefficientList[Series[Sinh[Exp[x] - 1]/Cosh[Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
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]!

Formula

E.g.f.: sinh(exp(x)-1)/cosh(exp(x)-1).

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.