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A295258 Expansion of e.g.f. coth(x)*(1 - sqrt(1 - 4*tanh(x)))/2. 5
1, 1, 4, 28, 304, 4456, 82144, 1827568, 47674624, 1427337856, 48248157184, 1817752215808, 75534405842944, 3432099993158656, 169290181445914624, 9009094978010165248, 514518446264601739264, 31389459744670699257856, 2037360033664565682110464, 140182487701223036287909888 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

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

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]!

CROSSREFS

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

Sequence in context: A307083 A274043 A007152 * A177554 A316212 A192485

Adjacent sequences:  A295255 A295256 A295257 * A295259 A295260 A295261

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 18 2017

STATUS

approved

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Last modified July 8 01:48 EDT 2020. Contains 335502 sequences. (Running on oeis4.)