A295256 Expansion of e.g.f. 2/(1 + sqrt(1 - 4*x*cosh(x))).

1, 1, 4, 33, 384, 5945, 115680, 2713417, 74568704, 2350925649, 83660474880, 3317599815761, 145087264278528, 6937450761100873, 360078818344534016, 20162761727269502265, 1211588127198611374080, 77769423447774393465377, 5310706204624302598127616, 384439720034220718046773249

Offset

0,3

Links

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

Formula

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

a(n) ~ sqrt(2 + 2*r*sqrt(1-16*r^2)) * n^(n-1) / (exp(n) * r^n), where r = 0.2428073624074744554637516823... is the root of the equation 2*r*(exp(2*r)+1) = exp(r). - Vaclav Kotesovec, Nov 18 2017

Maple

a:=series(2/(1+sqrt(1-4*x*cosh(x))), x=0, 21): seq(n!*coeff(a, x, n), n=0..19); # Paolo P. Lava, Mar 27 2019

Mathematica

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

Crossrefs

Cf. A000108, A295237, A295254, A295255, A295257, A295258.

Sequence in context: A166906 A293020 A293193 * A269926 A331794 A156132

Adjacent sequences: A295253 A295254 A295255 * A295257 A295258 A295259

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 18 2017

Status

approved