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 A127016 #10 Nov 22 2024 06:14:01
%S A127016 1,-7,42,-259,1582,-9702,59388,-363867,2228310,-13649650,83599852,
%T A127016 -512063790,3136339276,-19210260076,117662192928,-720683271819,
%U A127016 4414176556902,-27036862348986,165600668448348,-1014304512179994,6212613590747172,-38052263986931796
%N A127016 Expansion of 1/(1+7*x*c(x)), c(x) the g.f. of Catalan numbers A000108.
%C A127016 Hankel transform is (-7)^n.
%H A127016 G. C. Greubel, <a href="/A127016/b127016.txt">Table of n, a(n) for n = 0..1000</a>
%F A127016 a(n) = Sum_{k=0..n} A039599(n,k)*(-8)^k.
%F A127016 G.f.: 2/(9 - 7*sqrt(1-4*x)). - _G. C. Greubel_, May 31 2019
%F A127016 D-finite with recurrence 8*n*a(n) +(17*n+48)*a(n-1) +98*(-2*n+3)*a(n-2)=0. - _R. J. Mathar_, Nov 22 2024
%p A127016 c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+7*x*c),x=0,25): seq(coeff(ser,x,n),n=0..22); - _Emeric Deutsch_, Mar 27 2007
%t A127016 CoefficientList[Series[2/(9-7*Sqrt[1-4*x]), {x,0,30}], x] (* _G. C. Greubel_, May 31 2019 *)
%o A127016 (PARI) my(x='x+O('x^30)); Vec(2/(9-7*sqrt(1-4*x))) \\ _G. C. Greubel_, May 31 2019
%o A127016 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(9 - 7*Sqrt(1-4*x)) )); // _G. C. Greubel_, May 31 2019
%o A127016 (Sage) (2/(9-7*sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 31 2019
%K A127016 sign
%O A127016 0,2
%A A127016 _Philippe Deléham_, Mar 21 2007
%E A127016 More terms from _Emeric Deutsch_, Mar 27 2007