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 A127053 #15 Sep 08 2022 08:45:29
%S A127053 1,-9,72,-585,4734,-38358,310662,-2516481,20383110,-165104478,
%T A127053 1337341896,-10832484474,87743071332,-710719065000,5756823757890,
%U A127053 -46630274845905,377705217526470,-3059412293786310,24781239462988800,-200728040080084110,1625897123058144420
%N A127053 Expansion of 1/(1+9*x*c(x)), where c(x) = g.f. for Catalan numbers A000108.
%C A127053 Hankel transform is (-9)^n.
%H A127053 G. C. Greubel, <a href="/A127053/b127053.txt">Table of n, a(n) for n = 0..1000</a>
%F A127053 a(n) = Sum_{k=0..n} A039599(n,k)*(-10)^k.
%F A127053 G.f.: 2/(11 - 9*sqrt(1-4*x)). - _G. C. Greubel_, May 28 2019
%p A127053 c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+9*x*c),x=0,24): seq(coeff(ser,x,n),n=0..21); # _Emeric Deutsch_, Mar 23 2007
%t A127053 CoefficientList[Series[2/(11-9*Sqrt[1-4*x]), {x, 0, 30}], x] (* _G. C. Greubel_, May 28 2019 *)
%o A127053 (PARI) my(x='x+O('x^30)); Vec(2/(11-9*sqrt(1-4*x))) \\ _G. C. Greubel_, May 28 2019
%o A127053 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(11-9*Sqrt(1-4*x)) )); // _G. C. Greubel_, May 28 2019
%o A127053 (Sage) (2/(11-9*sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 28 2019
%Y A127053 Cf. A000108, A039599.
%K A127053 sign
%O A127053 0,2
%A A127053 _Philippe Deléham_, Mar 21 2007
%E A127053 More terms from _Emeric Deutsch_, Mar 23 2007