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 A383606 #17 May 06 2025 15:37:58
%S A383606 1,1,1,7,13,19,70,166,307,853,2164,4600,11491,29137,66808,161692,
%T A383606 403843,961129,2316238,5715742,13831219,33450073,82013692,199820584,
%U A383606 485389276,1187152906,2900334583,7069398325,17283884710,42278723290,103291322056,252668924536
%N A383606 Expansion of 1/( (1-x) * (1-x-9*x^3)^2 )^(1/3).
%H A383606 Vincenzo Librandi, <a href="/A383606/b383606.txt">Table of n, a(n) for n = 0..500</a>
%F A383606 a(n) = Sum_{k=0..floor(n/3)} (-9)^k * binomial(-2/3,k) * binomial(n-2*k,k).
%t A383606 CoefficientList[Series[1/((1-x)*(1-x-9*x^3)^2)^(1/3),{x,0,31}],x] (* _Stefano Spezia_, May 02 2025 *)
%t A383606 Table[Sum[(-9)^k*Binomial[-2/3,k]*Binomial[n-2*k,k],{k,0,Floor[n/3]}],{n,0,35}] (* _Vincenzo Librandi_, May 06 2025 *)
%o A383606 (PARI) a(n) = sum(k=0, n\3, (-9)^k*binomial(-2/3, k)*binomial(n-2*k, k));
%o A383606 (Magma) R<x>:=PowerSeriesRing(Rationals(), 35); Coefficients(R!( 1/( (1-x) * (1-x-9*x^3)^2 )^(1/3))); // _Vincenzo Librandi_, May 06 2025
%Y A383606 Cf. A383601, A383605.
%K A383606 nonn
%O A383606 0,4
%A A383606 _Seiichi Manyama_, May 01 2025