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 A053537 #22 Sep 08 2022 08:45:00
%S A053537 1,10,175,2500,38125,568750,8546875,128125000,1922265625,28832031250,
%T A053537 432490234375,6487304687500,97309814453125,1459645996093750,
%U A053537 21894696044921875,328420410156250000,4926306304931640625,73894593811035156250,1108418910980224609375
%N A053537 Expansion of 1/((1+5*x)*(1-15*x)).
%D A053537 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H A053537 G. C. Greubel, <a href="/A053537/b053537.txt">Table of n, a(n) for n = 0..845</a>
%H A053537 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,75).
%F A053537 a(n) = (5^n/4)*(3^(n+1) + (-1)^n).
%F A053537 a(n) = 10*a(n-1) + 75*a(n-2), with a(0)=1, a(1)=10.
%F A053537 E.g.f.: (3*exp(15*x) + exp(-5*x))/4. - _G. C. Greubel_, May 16 2019
%t A053537 LinearRecurrence[{10, 75}, {1, 10}, 30] (* _G. C. Greubel_, May 16 2019 *)
%t A053537 CoefficientList[Series[1/((1+5x)(1-15x)),{x,0,20}],x] (* _Harvey P. Dale_, Jun 15 2022 *)
%o A053537 (PARI) Vec(1/((1+5*x)*(1-15*x)) + O(x^30)) \\ _Michel Marcus_, Dec 03 2014
%o A053537 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/((1+5*x)*(1-15*x)) )); // _G. C. Greubel_, May 16 2019
%o A053537 (Sage) (1/((1+5*x)*(1-15*x))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 16 2019
%o A053537 (GAP) a:=[1,10];; for n in [3..30] do a[n]:=10*a[n-1]+75*a[n-2]; od; a; # _G. C. Greubel_, May 16 2019
%Y A053537 Cf. A015518.
%K A053537 easy,nonn
%O A053537 0,2
%A A053537 _Barry E. Williams_, Jan 15 2000
%E A053537 Terms a(11) onward added by _G. C. Greubel_, May 16 2019