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 A126982 #15 Nov 22 2024 06:09:20
%S A126982 1,-3,6,-15,30,-78,144,-423,630,-2490,1956,-16998,-5844,-142860,
%T A126982 -235740,-1475415,-3951450,-17627490,-57571740,-228692610,-810889020,
%U A126982 -3098590020,-11377872720,-43011709110,-160518364740,-606261789828
%N A126982 Expansion of 1/(1+3*x*c(x)), c(x) the g.f. of Catalan numbers A000108.
%C A126982 Hankel transform is (-3)^n.
%C A126982 Catalan transform of the sequence (-1)^n*A000244(n). - _R. J. Mathar_, Nov 11 2008
%H A126982 G. C. Greubel, <a href="/A126982/b126982.txt">Table of n, a(n) for n = 0..1000</a>
%F A126982 a(n) = Sum_{k=0..n} A039599(n,k)*(-4)^k.
%F A126982 G.f.: 2/(5 - 3*sqrt(1-4*x)). - _G. C. Greubel_, May 28 2019
%F A126982 D-finite with recurrence 4*n*a(n) +(-7*n+24)*a(n-1) +18*(-2*n+3)*a(n-2)=0. - _R. J. Mathar_, Nov 22 2024
%t A126982 CoefficientList[Series[2/(5-3*Sqrt[1-4*x]), {x,0,30}], x] (* _G. C. Greubel_, May 28 2019 *)
%o A126982 (PARI) my(x='x+O('x^30)); Vec(2/(5-3*sqrt(1-4*x))) \\ _G. C. Greubel_, May 28 2019
%o A126982 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(5-3*Sqrt(1-4*x)) )); // _G. C. Greubel_, May 28 2019
%o A126982 (Sage) (2/(5-3*sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 28 2019
%Y A126982 Cf. A000108, A000244, A039599.
%K A126982 sign
%O A126982 0,2
%A A126982 _Philippe Deléham_, Mar 21 2007
%E A126982 Extended by _R. J. Mathar_, Nov 11 2008