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 A383604 #18 May 06 2025 09:32:51
%S A383604 1,1,1,4,7,10,31,70,127,328,799,1666,4000,9817,22078,52060,126727,
%T A383604 296101,699601,1691350,4024450,9574393,23081776,55394488,132650923,
%U A383604 319807159,770872429,1855190146,4479086230,10825202521,26145137668,63241928080,153144714331
%N A383604 Expansion of 1/( (1-x)^2 * (1-x-9*x^3) )^(1/3).
%H A383604 Vincenzo Librandi, <a href="/A383604/b383604.txt">Table of n, a(n) for n = 0..500</a>
%F A383604 a(n) = Sum_{k=0..floor(n/3)} (-9)^k * binomial(-1/3,k) * binomial(n-2*k,k).
%t A383604 CoefficientList[Series[1/((1-x)^2*(1-x-9*x^3))^(1/3),{x,0,32}],x] (* _Stefano Spezia_, May 02 2025 *)
%t A383604 Table[Sum[(-9)^k*Binomial[-1/3,k]*Binomial[n-2*k,k],{k,0,Floor[n/3]}],{n,0,35}] (* _Vincenzo Librandi_, May 06 2025 *)
%o A383604 (PARI) a(n) = sum(k=0, n\3, (-9)^k*binomial(-1/3, k)*binomial(n-2*k, k));
%o A383604 (Magma) R<x>:=PowerSeriesRing(Rationals(), 35); Coefficients(R!( 1/( (1-x)^2 * (1-x-9*x^3) )^(1/3))); // _Vincenzo Librandi_, May 06 2025
%Y A383604 Cf. A383597, A383603.
%Y A383604 Cf. A217615.
%K A383604 nonn
%O A383604 0,4
%A A383604 _Seiichi Manyama_, May 01 2025