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 A383503 #35 May 07 2025 08:27:00
%S A383503 1,2,3,10,23,42,97,218,435,918,1977,4062,8393,17590,36303,74614,
%T A383503 154211,317334,650505,1335054,2736453,5595950,11439475,23370270,
%U A383503 47681965,97217882,198110199,403383026,820820215,1669405626,3393344257,6893850650,13999109715,28414742790
%N A383503 Expansion of 1/sqrt( (1-x) * (1-x-4*x^3)^3 ).
%H A383503 Vincenzo Librandi, <a href="/A383503/b383503.txt">Table of n, a(n) for n = 0..1000</a>
%F A383503 a(n) = Sum_{k=0..floor(n/3)} (2*k+1) * binomial(2*k,k) * binomial(n-2*k+1,k+1).
%t A383503 Table[Sum[(2*k+1)*Binomial[2*k,k]*Binomial[n-2*k+1,k+1],{k,0,Floor[n/3]}],{n,0,35}] (* _Vincenzo Librandi_, May 06 2025 *)
%o A383503 (PARI) a(n) = sum(k=0, n\3, (2*k+1)*binomial(2*k, k)*binomial(n-2*k+1, k+1));
%o A383503 (Magma) R<x>:=PowerSeriesRing(Rationals(), 35); Coefficients(R!( 1/Sqrt( (1-x) * (1-x-4*x^3)^3 ))); // _Vincenzo Librandi_, May 06 2025
%Y A383503 Cf. A383254, A383499.
%Y A383503 Cf. A217615, A377213.
%K A383503 nonn
%O A383503 0,2
%A A383503 _Seiichi Manyama_, May 05 2025