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 A383598 #17 May 04 2025 08:50:05
%S A383598 1,3,19,132,1000,7884,63802,525666,4388518,37010220,314633944,
%T A383598 2692239012,23161121641,200158043223,1736461678195,15114944308560,
%U A383598 131950690469920,1154858014686960,10130508263000440,89045875688728440,784127521246844872,6916291864328172336
%N A383598 Expansion of 1/( (1-x^2)^2 * (1-x^2-9*x) )^(1/3).
%H A383598 Vincenzo Librandi, <a href="/A383598/b383598.txt">Table of n, a(n) for n = 0..300</a>
%F A383598 a(n) = Sum_{k=0..floor(n/2)} (-9)^(n-2*k) * binomial(-1/3,n-2*k) * binomial(n-k,k).
%F A383598 a(n) ~ ((9 + sqrt(85))/2)^(n+1) / (Gamma(1/3) * 3^(4/3) * 85^(1/6) * n^(2/3)). - _Vaclav Kotesovec_, May 02 2025
%t A383598 Table[Sum[(-9)^(n-2*k)* Binomial[-1/3, n-2*k]* Binomial[n-k,k],{k,0,Floor[n/2]}],{n,0,22}] (* _Vincenzo Librandi_, May 04 2025 *)
%o A383598 (PARI) a(n) = sum(k=0, n\2, (-9)^(n-2*k)*binomial(-1/3, n-2*k)*binomial(n-k, k));
%o A383598 (Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/( (1-x^2)^2 * (1-x^2-9*x) )^(1/3))); // _Vincenzo Librandi_, May 04 2025
%Y A383598 Cf. A383597, A383599.
%Y A383598 Cf. A376805.
%K A383598 nonn
%O A383598 0,2
%A A383598 _Seiichi Manyama_, May 01 2025