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 A372023 #12 Apr 16 2024 10:26:36
%S A372023 1,2,0,2,-2,6,-12,30,-72,182,-464,1206,-3170,8426,-22596,61074,
%T A372023 -166194,454950,-1251984,3461574,-9611190,26787378,-74916660,
%U A372023 210178458,-591347988,1668172842,-4717282752,13369522250,-37970114702,108045430902,-308001125516
%N A372023 Expansion of ( (1 + 3*x)/(1 - x) )^(1/2).
%F A372023 a(n) = Sum_{k=0..n} 4^k * binomial(1/2,k) * binomial(n-1,n-k).
%F A372023 a(n) = (-1)^(n-1) * 2 * A005043(n-1) for n > 0.
%F A372023 a(n) ~ (-1)^(n+1) * 3^(n + 1/2) / (4*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Apr 16 2024
%o A372023 (PARI) my(N=40, x='x+O('x^N)); Vec(sqrt((1+3*x)/(1-x)))
%o A372023 (PARI) a(n) = sum(k=0, n, 4^k*binomial(1/2, k)*binomial(n-1, n-k));
%Y A372023 Cf. A005043, A103872, A372024.
%K A372023 sign
%O A372023 0,2
%A A372023 _Seiichi Manyama_, Apr 16 2024