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 A360133 #24 Jul 12 2024 10:17:26
%S A360133 1,2,0,-4,-4,6,18,4,-48,-70,60,288,170,-686,-1386,432,4928,4806,-9684,
%T A360133 -27572,-3672,84106,118162,-122388,-537834,-284830,1386840,2688944,
%U A360133 -1103362,-10181934,-9354198,21404728,57921144,3663942,-185437360,-248708676,292137656
%N A360133 Expansion of 1/sqrt(1 - 4*x/(1+x)^3).
%H A360133 Seiichi Manyama, <a href="/A360133/b360133.txt">Table of n, a(n) for n = 0..1000</a>
%F A360133 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(2*k,k) * binomial(n+2*k-1,n-k).
%F A360133 n*a(n) = -( -2*a(n-1) + (2*n)*a(n-2) + 4*(n-3)*a(n-3) + (n-4)*a(n-4) ) for n > 3.
%F A360133 a(0) = 1; a(n) = (2/n) * Sum_{k=0..n-1} (-1)^(n-1-k) * (n+k) * binomial(n+1-k,2) * a(k).
%F A360133 a(n) = (-1)^(n+1)*n*(n + 1)*hypergeom([3/2, 1-n, 1+n/2, (3+n)/2], [4/3, 5/3, 2], 2^4/3^3) for n > 0. - _Stefano Spezia_, Jul 11 2024
%t A360133 a[n_]:=(-1)^(n+1)n(n+1)HypergeometricPFQ[{3/2,1-n,1+n/2,(3+n)/2}, {4/3,5/3,2}, 2^4/3^3]; Join[{1},Array[a,36]] (* _Stefano Spezia_, Jul 11 2024 *)
%o A360133 (PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1+x)^3))
%Y A360133 Cf. A006139, A137635, A361790, A361791, A361792.
%K A360133 sign
%O A360133 0,2
%A A360133 _Seiichi Manyama_, Mar 24 2023