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 A114194 #14 May 24 2024 15:14:22
%S A114194 1,-2,9,-46,261,-1578,9969,-65030,434685,-2961922,20497577,-143673630,
%T A114194 1017887989,-7277385306,52438781409,-380442087606,2776651758189,
%U A114194 -20372853020466,150186005826969,-1111840965284046,8262492144613989,-61614023992470666,460907701311527889
%N A114194 Expansion of 1/(1+x*(2-x)*c(-2*x)), c(x) the g.f. of A000108.
%C A114194 Diagonal sums of A114193.
%H A114194 G. C. Greubel, <a href="/A114194/b114194.txt">Table of n, a(n) for n = 0..1000</a>
%F A114194 G.f.: 4/(2+x-(x-2)*sqrt(1+8*x)).
%F A114194 Conjecture: 6*(n+1)*a(n) + (37n-29)*a(n-1) + 2*(45-41n)*a(n-2) + (47n-87)*a(n-3) + 4*(5-2n)*a(n-4) = 0. - _R. J. Mathar_, Dec 10 2011
%F A114194 a(n) ~ 17 * (-1)^n * 2^(3*n+4) / (225 * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Feb 03 2014
%t A114194 CoefficientList[Series[4/(2+x-(x-2)*Sqrt[1+8*x]), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 03 2014 *)
%o A114194 (PARI) x='x+O('x^50); Vec(4/(2+x-(x-2)*sqrt(1+8*x))) \\ _G. C. Greubel_, Mar 17 2017
%Y A114194 Cf. A000108, A114193.
%K A114194 easy,sign
%O A114194 0,2
%A A114194 _Paul Barry_, Nov 16 2005