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 A365183 #24 Jan 10 2025 11:24:32
%S A365183 1,1,5,34,268,2299,20838,196326,1903524,18868861,190356231,1948055058,
%T A365183 20173907384,211020478270,2226243632838,23660868061422,
%U A365183 253099278807684,2722819049879436,29439894433161189,319749417998303470,3486914150183526920
%N A365183 G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x*A(x)^4).
%H A365183 Seiichi Manyama, <a href="/A365183/b365183.txt">Table of n, a(n) for n = 0..939</a>
%H A365183 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 A365183 a(n) = (1/(4*n+1)) * Sum_{k=0..floor(n/2)} binomial(n-k,k) * binomial(4*n+1,n-k).
%o A365183 (PARI) a(n) = sum(k=0, n\2, binomial(n-k, k)*binomial(4*n+1, n-k))/(4*n+1);
%Y A365183 Cf. A002294, A365178, A365180, A365181, A365182.
%Y A365183 Cf. A006605, A255673, A365189.
%Y A365183 Cf. A364989.
%K A365183 nonn
%O A365183 0,3
%A A365183 _Seiichi Manyama_, Aug 25 2023