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 A365690 #10 Sep 16 2023 10:41:27
%S A365690 1,0,1,1,5,10,38,101,353,1070,3659,11843,40505,135873,468104,1604375,
%T A365690 5576315,19386656,67950717,238676813,842797959,2983745508,10603445402,
%U A365690 37777263153,134985354179,483438728094,1735527037388,6243193190117,22503637842423
%N A365690 G.f. satisfies A(x) = 1 + x^2*A(x)^4 / (1 - x*A(x)).
%F A365690 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k-1,n-2*k) * binomial(n+2*k+1,k) / (n+2*k+1).
%o A365690 (PARI) a(n) = sum(k=0, n\2, binomial(n-k-1, n-2*k)*binomial(n+2*k+1, k)/(n+2*k+1));
%Y A365690 Cf. A004148, A005043, A025246, A046736, A365691.
%Y A365690 Cf. A365692.
%K A365690 nonn
%O A365690 0,5
%A A365690 _Seiichi Manyama_, Sep 16 2023