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 A365733 #17 Sep 18 2023 08:59:23
%S A365733 1,1,1,1,1,1,2,6,16,36,71,127,215,367,676,1376,2982,6514,13855,28407,
%T A365733 56543,111127,219918,444450,919744,1933732,4082467,8576027,17861347,
%U A365733 36938427,76207797,157652981,328119005,687377565,1446665765,3050094661,6427116181
%N A365733 G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^5*A(x)^3).
%H A365733 Seiichi Manyama, <a href="/A365733/b365733.txt">Table of n, a(n) for n = 0..1000</a>
%F A365733 a(n) = Sum_{k=0..floor(n/6)} binomial(n-5*k,k) * binomial(n-2*k+1,n-5*k) / (n-2*k+1) = Sum_{k=0..floor(n/6)} binomial(n-2*k,4*k) * binomial(4*k,k) / (3*k+1).
%o A365733 (PARI) a(n) = sum(k=0, n\6, binomial(n-5*k, k)*binomial(n-2*k+1, n-5*k)/(n-2*k+1));
%Y A365733 Cf. A127902, A186996, A215340, A365079.
%Y A365733 Cf. A002293, A365735.
%K A365733 nonn
%O A365733 0,7
%A A365733 _Seiichi Manyama_, Sep 17 2023