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 A383599 #14 May 04 2025 14:44:30
%S A383599 1,3,18,127,951,7425,59473,484902,4005720,33425587,281152551,
%T A383599 2380227705,20259341335,173218395228,1486747223136,12803424371263,
%U A383599 110579924167533,957494150283249,8309596928695417,72260720257071936,629526082305028041,5493357757059584986
%N A383599 Expansion of 1/( (1-x^3)^2 * (1-x^3-9*x) )^(1/3).
%H A383599 Vincenzo Librandi, <a href="/A383599/b383599.txt">Table of n, a(n) for n = 0..300</a>
%F A383599 a(n) = Sum_{k=0..floor(n/3)} (-9)^(n-3*k) * binomial(-1/3,n-3*k) * binomial(n-2*k,k).
%t A383599 Table[Sum[(-9)^(n-3*k)* Binomial[-1/3, n-3*k]* Binomial[n-2*k,k],{k,0,Floor[n/3]}],{n,0,22}] (* _Vincenzo Librandi_, May 04 2025 *)
%o A383599 (PARI) a(n) = sum(k=0, n\3, (-9)^(n-3*k)*binomial(-1/3, n-3*k)*binomial(n-2*k, k));
%o A383599 (Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/( (1-x^3)^2 * (1-x^3-9*x) )^(1/3))); // _Vincenzo Librandi_, May 04 2025
%Y A383599 Cf. A383597, A383598.
%Y A383599 Cf. A376806.
%K A383599 nonn
%O A383599 0,2
%A A383599 _Seiichi Manyama_, May 01 2025