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 A365691 #10 Sep 16 2023 10:41:47
%S A365691 1,0,1,1,6,12,54,147,593,1886,7292,25204,96153,348304,1327716,4946471,
%T A365691 18936366,71827598,276612103,1062220253,4115807184,15947902376,
%U A365691 62148513732,242485933208,949828266722,3726623622402,14663689944397,57798199213989
%N A365691 G.f. satisfies A(x) = 1 + x^2*A(x)^5 / (1 - x*A(x)).
%F A365691 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k-1,n-2*k) * binomial(n+3*k+1,k) / (n+3*k+1).
%o A365691 (PARI) a(n) = sum(k=0, n\2, binomial(n-k-1, n-2*k)*binomial(n+3*k+1, k)/(n+3*k+1));
%Y A365691 Cf. A004148, A005043, A025246, A046736, A365690.
%Y A365691 Cf. A365693.
%K A365691 nonn
%O A365691 0,5
%A A365691 _Seiichi Manyama_, Sep 16 2023