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 A114190 #14 Mar 17 2017 22:09:24
%S A114190 1,-1,4,-17,87,-490,2945,-18517,120340,-802005,5451651,-37652546,
%T A114190 263480357,-1864065017,13311094644,-95816113129,694511157535,
%U A114190 -5064818563258,37135165923801,-273581694291309,2024194855052180,-15034769479254861,112062948489702251,-837936593024505298
%N A114190 Expansion of 1/(1+x*(1-x)*c(-2*x)), c(x) the g.f. of A000108.
%C A114190 Diagonal sums of A114189. Alternating sign version of A110508.
%H A114190 G. C. Greubel, <a href="/A114190/b114190.txt">Table of n, a(n) for n = 0..1000</a>
%F A114190 G.f.: 4/(3+x+(1-x)*sqrt(1+8*x)).
%F A114190 Conjecture: n*a(n) +(7n-10)*a(n-1) +2*(14-3n)*a(n-2) +(13n-20)*a(n-3) +(66-23n)*a(n-4) +4*(2n-7)*a(n-5)=0. - R. J. Mathar, Dec 10 2011
%F A114190 a(n) ~ 9 * (-1)^n * 2^(3*n+4) / (529 * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Feb 03 2014
%t A114190 CoefficientList[Series[4/(3+x+(1-x)*Sqrt[1+8*x]), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 03 2014 *)
%o A114190 (PARI) x='x+O('x^50); Vec(4/(3+x+(1-x)*sqrt(1+8*x))) \\ _G. C. Greubel_, Mar 17 2017
%K A114190 easy,sign
%O A114190 0,3
%A A114190 _Paul Barry_, Nov 16 2005