|
%I #9 Mar 27 2019 10:02:30
%S 1,1,4,28,304,4456,82144,1827568,47674624,1427337856,48248157184,
%T 1817752215808,75534405842944,3432099993158656,169290181445914624,
%U 9009094978010165248,514518446264601739264,31389459744670699257856,2037360033664565682110464,140182487701223036287909888
%N Expansion of e.g.f. coth(x)*(1 - sqrt(1 - 4*tanh(x)))/2.
%F E.g.f.: 1/(1 - tanh(x)/(1 - tanh(x)/(1 - tanh(x)/(1 - tanh(x)/(1 - ...))))), a continued fraction.
%F a(n) ~ sqrt(15) * 2^(n-1) * n^(n-1) / (exp(n) * (log(5/3))^(n - 1/2)). - _Vaclav Kotesovec_, Nov 18 2017
%p a:=series(coth(x)*(1-sqrt(1-4*tanh(x)))/2,x=0,21): seq(n!*coeff(a,x,n),n=0..19); # _Paolo P. Lava_, Mar 27 2019
%t nmax = 19; CoefficientList[Series[Coth[x] (1 - Sqrt[1 - 4 Tanh[x]])/2, {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 19; CoefficientList[Series[1/(1 + ContinuedFractionK[-Tanh[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A000108, A295237, A295254, A295255, A295256, A295257.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Nov 18 2017
|
