login
A296543
Expansion of e.g.f. tanh(exp(x)-1).
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
0,5
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.
EXAMPLE
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! + ...
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]!
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 15 2017
STATUS
approved