This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A295256 #14 Feb 24 2025 05:46:29
%S A295256 1,1,4,33,384,5945,115680,2713417,74568704,2350925649,83660474880,
%T A295256 3317599815761,145087264278528,6937450761100873,360078818344534016,
%U A295256 20162761727269502265,1211588127198611374080,77769423447774393465377,5310706204624302598127616,384439720034220718046773249
%N A295256 Expansion of e.g.f. 2/(1 + sqrt(1 - 4*x*cosh(x))).
%F A295256 E.g.f.: 1/(1 - x*cosh(x)/(1 - x*cosh(x)/(1 - x*cosh(x)/(1 - x*cosh(x)/(1 - ...))))), a continued fraction.
%F A295256 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
%F A295256 a(n) = Sum_{k=0..n} k! * binomial(2*k+1,k)/(2*k+1) * A185951(n,k). - _Seiichi Manyama_, Feb 23 2025
%p A295256 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
%t A295256 nmax = 19; CoefficientList[Series[2/(1 + Sqrt[1 - 4 x Cosh[x]]), {x, 0, nmax}], x] Range[0, nmax]!
%t A295256 nmax = 19; CoefficientList[Series[1/(1 + ContinuedFractionK[-x Cosh[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
%Y A295256 Cf. A000108, A185951, A295237, A295254, A295255, A295257, A295258.
%K A295256 nonn
%O A295256 0,3
%A A295256 _Ilya Gutkovskiy_, Nov 18 2017