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 A026853 #15 Nov 22 2024 07:14:40
%S A026853 1,10,66,365,1837,8741,40133,179932,793605,3460106,14961664,64306917,
%T A026853 275180827,1173714565,4994096327,21211537533,89972566673,381261067469,
%U A026853 1614446775255,6832832045575,28908094009481,122272843951891,517095189163181
%N A026853 a(n) = T(2n,n+4), T given by A026736.
%H A026853 G. C. Greubel, <a href="/A026853/b026853.txt">Table of n, a(n) for n = 4..1000</a>
%F A026853 G.f.: x^4*C(x)^9/(1 -x/sqrt(1-4*x)), where C(x) if the g.f. for Catalan numbers A000108. - _G. C. Greubel_, Jul 17 2019
%F A026853 a(n) ~ (3 - sqrt(5))^9 * (2 + sqrt(5))^(n+4) / (512*sqrt(5)). - _Vaclav Kotesovec_, Jul 18 2019
%F A026853 D-finite with recurrence -(n+5)*(3013*n-9152)*a(n) +2*(15151*n^2+5919*n-112720)*a(n-1) +2*(-35029*n^2+9054*n-235442)*a(n-2) +6*(-19475*n^2+144598*n+188045)*a(n-3) +3*(131869*n^2-942353*n+1922276)*a(n-4) +2*(2*n-7)*(24721*n-92359)*a(n-5)=0. - _R. J. Mathar_, Nov 22 2024
%t A026853 Drop[CoefficientList[Series[Sqrt[1-4x]*(1-Sqrt[1-4x])^9/(512*x^5*(Sqrt[1-4x]-x)), {x,0,40}], x], 4] (* _G. C. Greubel_, Jul 17 2019 *)
%o A026853 (PARI) my(x='x+O('x^40)); Vec(sqrt(1-4*x)*(1-sqrt(1-4*x))^9/(512*x^5*(sqrt(1-4*x) -x)) ) \\ _G. C. Greubel_, Jul 17 2019
%o A026853 (Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( Sqrt(1-4*x)*(1-Sqrt(1-4*x))^9/(512*x^5*(Sqrt(1-4*x) -x)) )); // _G. C. Greubel_, Jul 17 2019
%o A026853 (Sage) a=(sqrt(1-4*x)*(1-sqrt(1-4*x))^9/(512*x^5*(sqrt(1-4*x)-x))).series(x, 40).coefficients(x, sparse=False); a[4:] # _G. C. Greubel_, Jul 17 2019
%Y A026853 Cf. A000108, A026736.
%K A026853 nonn
%O A026853 4,2
%A A026853 _Clark Kimberling_