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 A126985 #20 Nov 22 2024 06:17:35
%S A126985 1,-8,56,-400,2840,-20208,143664,-1021728,7265240,-51665200,367392656,
%T A126985 -2612584928,18578329456,-132112749920,939467783520,-6680662171200,
%U A126985 47506922377560,-337827035002800,2402325467002320,-17083203745473120,121480558396908240,-863861754435010080
%N A126985 Expansion of 1/(1+8*x*c(x)), c(x) the g.f. of Catalan numbers A000108.
%C A126985 Hankel transform is (-8)^n.
%C A126985 Catalan transform of (-1)^n*A001018(n). - _R. J. Mathar_, Nov 11 2008
%H A126985 G. C. Greubel, <a href="/A126985/b126985.txt">Table of n, a(n) for n = 0..1000</a>
%F A126985 a(n) = Sum_{k=0..n} A039599(n,k)*(-9)^k.
%F A126985 G.f.: 2/(10 - 8*sqrt(1-4*x)). - _G. C. Greubel_, May 28 2019
%F A126985 D-finite with recurrence 9*n*a(n) +2*(14*n+27)*a(n-1) +128*(-2*n+3)*a(n-2)=0. - _R. J. Mathar_, Nov 22 2024
%p A126985 c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+8*x*c),x=0,25): seq(coeff(ser,x,n),n=0..21); # _Emeric Deutsch_, Mar 24 2007
%t A126985 CoefficientList[Series[2/(10-8*Sqrt[1-4*x]), {x,0,30}], x] (* _G. C. Greubel_, May 28 2019 *)
%o A126985 (PARI) my(x='x+O('x^30)); Vec(2/(10-8*sqrt(1-4*x))) \\ _G. C. Greubel_, May 28 2019
%o A126985 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(10-8*Sqrt(1-4*x)) )); // _G. C. Greubel_, May 28 2019
%o A126985 (Sage) (2/(10-8*sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 28 2019
%Y A126985 Cf. A000108, A001018, A039599.
%K A126985 sign
%O A126985 0,2
%A A126985 _Philippe Deléham_, Mar 21 2007
%E A126985 More terms from _Emeric Deutsch_, Mar 24 2007