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 A295254 #13 Feb 24 2025 05:45:52
%S A295254 1,1,4,31,352,5341,101824,2341291,63092992,1950837241,68093599744,
%T A295254 2648776394551,113633946898432,5330308817264341,271416230974603264,
%U A295254 14910196369733535811,879003840976919068672,55354496206857969062641,3708594029795800700944384,263391744037123969891925071
%N A295254 Expansion of e.g.f. csch(x)*(1 - sqrt(1 - 4*sinh(x)))/2.
%F A295254 E.g.f.: 1/(1 - sinh(x)/(1 - sinh(x)/(1 - sinh(x)/(1 - sinh(x)/(1 - ...))))), a continued fraction.
%F A295254 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
%F A295254 a(n) = Sum_{k=0..n} k! * binomial(2*k+1,k)/(2*k+1) * A136630(n,k). - _Seiichi Manyama_, Feb 23 2025
%p A295254 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
%t A295254 nmax = 19; CoefficientList[Series[Csch[x] (1 - Sqrt[1 - 4 Sinh[x]])/2, {x, 0, nmax}], x] Range[0, nmax]!
%t A295254 nmax = 19; CoefficientList[Series[1/(1 + ContinuedFractionK[-Sinh[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
%Y A295254 Cf. A000108, A136630, A295237, A295255, A295256, A295257, A295258.
%K A295254 nonn
%O A295254 0,3
%A A295254 _Ilya Gutkovskiy_, Nov 18 2017