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 A366433 #13 Oct 10 2023 05:09:52
%S A366433 1,1,-3,9,-37,171,-849,4421,-23820,131676,-742616,4255944,-24714276,
%T A366433 145103426,-859920585,5137093695,-30902681230,187034086170,
%U A366433 -1138106903928,6958662440416,-42729903714420,263400623938140,-1629378251621535,10111374706286895
%N A366433 G.f. A(x) satisfies A(x) = 1 + x * ((1 - x) / A(x))^(3/2).
%F A366433 a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(5*k/2-1,k) * binomial(3*k/2,n-k) / (5*k/2-1).
%F A366433 a(n) ~ -(-1)^n * sqrt(4*10^(1/3) + 10^(2/3) - 5) * 3^(n + 1/2) * 5^(n-1) / (sqrt(Pi) * (2 + 10^(1/3)) * n^(3/2) * (4*10^(1/3) + 10^(2/3) - 11)^n). - _Vaclav Kotesovec_, Oct 10 2023
%t A366433 Table[(-1)^(n-1) * Sum[Binomial[5*k/2 - 1, k]*Binomial[3*k/2, n - k]/(5*k/2 - 1), {k, 0, n}], {n, 0, 30}] (* _Vaclav Kotesovec_, Oct 10 2023 *)
%o A366433 (PARI) a(n) = (-1)^(n-1)*sum(k=0, n, binomial(5*k/2-1, k)*binomial(3*k/2, n-k)/(5*k/2-1));
%Y A366433 Partial sums give A366404.
%Y A366433 Cf. A366431, A366432, A366434, A366435, A366436, A366437.
%K A366433 sign
%O A366433 0,3
%A A366433 _Seiichi Manyama_, Oct 09 2023