A295254 Expansion of e.g.f. csch(x)*(1 - sqrt(1 - 4*sinh(x)))/2.

1, 1, 4, 31, 352, 5341, 101824, 2341291, 63092992, 1950837241, 68093599744, 2648776394551, 113633946898432, 5330308817264341, 271416230974603264, 14910196369733535811, 879003840976919068672, 55354496206857969062641, 3708594029795800700944384, 263391744037123969891925071

Offset

0,3

Links

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

Formula

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

a(n) ~ sqrt(2) * 17^(1/4) * n^(n-1) / (exp(n) * (log((1+ sqrt(17))/4))^(n - 1/2)). - Vaclav Kotesovec, Nov 18 2017

Maple

a:=series(csch(x)*(1-sqrt(1-4*sinh(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[Csch[x] (1 - Sqrt[1 - 4 Sinh[x]])/2, {x, 0, nmax}], x] Range[0, nmax]!
nmax = 19; CoefficientList[Series[1/(1 + ContinuedFractionK[-Sinh[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A000108, A295237, A295255, A295256, A295257, A295258.

Sequence in context: A136728 A321031 A102757 * A343832 A145561 A201628

Adjacent sequences: A295251 A295252 A295253 * A295255 A295256 A295257

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 18 2017

Status

approved