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 A005053 #39 Sep 08 2022 08:44:33
%S A005053 1,3,15,75,375,1875,9375,46875,234375,1171875,5859375,29296875,
%T A005053 146484375,732421875,3662109375,18310546875,91552734375,457763671875,
%U A005053 2288818359375,11444091796875,57220458984375
%N A005053 Expand (1-2*x)/(1-5*x).
%C A005053 a(n) is the number of generalized compositions of n when there are 3*2^(i-1) different types of i, (i=1,2,...). - _Milan Janjic_, Sep 24 2010
%C A005053 INVERTi transform of A180034: (1, 4, 22, 124, 700, ...). - _Gary W. Adamson_, Aug 10 2016
%H A005053 G. C. Greubel, <a href="/A005053/b005053.txt">Table of n, a(n) for n = 0..1000</a>
%H A005053 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A005053 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=883">Encyclopedia of Combinatorial Structures 883</a>
%F A005053 Binomial transform of A122117. - _Philippe Deléham_, Oct 19 2006
%F A005053 a(0) = 1, a(n) = 3*5^(n-1) for n >= 1. - _Philippe Deléham_, Oct 19 2006
%F A005053 E.g.f.: (2 + 3*exp(5*x))/5. - _Ilya Gutkovskiy_, Aug 11 2016
%t A005053 CoefficientList[Series[(1-2x)/(1-5x),{x,0,30}],x] (* or *) Join[{1}, NestList[5#&,3,29]] (* _Harvey P. Dale_, Apr 25 2011 *)
%o A005053 (Magma) [ n eq 0 select 1 else 3*5^(n-1): n in [0..20] ]; // _Klaus Brockhaus_, Apr 04 2010
%o A005053 (PARI) x='x+O('x^50); Vec((1-2*x)/(1-5*x)) \\ _G. C. Greubel_, Sep 15 2017
%Y A005053 Cf. A180034.
%K A005053 nonn,easy
%O A005053 0,2
%A A005053 _N. J. A. Sloane_
%E A005053 Wrong formula deleted by _Klaus Brockhaus_, Apr 04 2010