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 A127680 #20 Nov 27 2023 12:21:44
%S A127680 1,1,2,4,8,17,35,74,154,324,677,1422,2977,6246,13086,27444,57518,
%T A127680 120600,252794,529994,1111013,2329187,4882755,10236280,21458943,
%U A127680 44986461,94308415,197707134,414469000,868886834,1821517772,3818600772
%N A127680 a(0) = 1; a(n+1) = Sum_{k=0..n} a(n-k)*a(floor(k/2)).
%H A127680 Seiichi Manyama, <a href="/A127680/b127680.txt">Table of n, a(n) for n = 0..1000</a>
%F A127680 G.f. A(x) satisfies: A(x) = 1 / (1 - x * (1 + x) * A(x^2)). - _Ilya Gutkovskiy_, Nov 15 2021
%F A127680 a(n) ~ c * d^n, where d = 2.096382783759695271747034891835844892559952962948180418542044889824924... and c = 0.413348184087944400305975399220165744000861336139702047444087822224828... - _Vaclav Kotesovec_, Nov 16 2021
%t A127680 f[l_List] := Block[{n = Length[l] - 1},Append[l, Sum[l[[n - k + 1]]*l[[Floor[k/2] + 1]], {k, 0, n}]]];Nest[f, {1}, 33] (* _Ray Chandler_, Feb 13 2007 *)
%Y A127680 Cf. A367652, A367653, A367654.
%Y A127680 Cf. A127681.
%K A127680 easy,nonn
%O A127680 0,3
%A A127680 _Leroy Quet_, Jan 23 2007
%E A127680 Extended by _Ray Chandler_, Feb 13 2007