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 A365189 #23 Jan 10 2025 11:24:36
%S A365189 1,1,6,50,485,5130,57391,667777,7999095,97986680,1221813880,
%T A365189 15456556791,197887386913,2559189842240,33383097891135,
%U A365189 438714241508615,5803049210371375,77199163872173757,1032215519193531310,13864180990526161995,186975433988014039830
%N A365189 G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)^5).
%H A365189 Seiichi Manyama, <a href="/A365189/b365189.txt">Table of n, a(n) for n = 0..864</a>
%H A365189 Jun Yan, <a href="https://arxiv.org/abs/2501.01152">Lattice paths enumerations weighted by ascent lengths</a>, arXiv:2501.01152 [math.CO], 2025. See p. 13.
%F A365189 a(n) = (1/(5*n+1)) * Sum_{k=0..floor(n/2)} binomial(n-k,k) * binomial(5*n+1,n-k).
%o A365189 (PARI) a(n) = sum(k=0, n\2, binomial(n-k, k)*binomial(5*n+1, n-k))/(5*n+1);
%Y A365189 Cf. A002295, A365184, A365185, A365186, A365187, A365188.
%Y A365189 Cf. A006605, A255673, A365183.
%K A365189 nonn
%O A365189 0,3
%A A365189 _Seiichi Manyama_, Aug 25 2023