A295258 Expansion of e.g.f. coth(x)*(1 - sqrt(1 - 4*tanh(x)))/2.

1, 1, 4, 28, 304, 4456, 82144, 1827568, 47674624, 1427337856, 48248157184, 1817752215808, 75534405842944, 3432099993158656, 169290181445914624, 9009094978010165248, 514518446264601739264, 31389459744670699257856, 2037360033664565682110464, 140182487701223036287909888

Offset: 0

Author

Ilya Gutkovskiy, Nov 18 2017

Keywords

• nonn

Crossrefs

Cf. A000108, A295237, A295254, A295255, A295256, A295257.

Programs

Maple

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

Mathematica

nmax = 19; CoefficientList[Series[Coth[x] (1 - Sqrt[1 - 4 Tanh[x]])/2, {x, 0, nmax}], x] Range[0, nmax]!
nmax = 19; CoefficientList[Series[1/(1 + ContinuedFractionK[-Tanh[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

Formula

E.g.f.: 1/(1 - tanh(x)/(1 - tanh(x)/(1 - tanh(x)/(1 - tanh(x)/(1 - ...))))), a continued fraction.

a(n) ~ sqrt(15) * 2^(n-1) * n^(n-1) / (exp(n) * (log(5/3))^(n - 1/2)). - Vaclav Kotesovec, Nov 18 2017