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 A371676 #16 Jan 10 2025 12:06:31
%S A371676 1,4,40,524,7824,126228,2143544,37750812,683194912,12628104740,
%T A371676 237388091208,4524456276524,87228274533040,1698091537435444,
%U A371676 33332913873239640,659038408936005692,13112372856351746112,262338658739430857796,5274545338183090647656
%N A371676 G.f. satisfies A(x) = 1 + x * A(x)^2 * (1 + A(x)^(1/2))^2.
%H A371676 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. 7.
%F A371676 G.f. satisfies A(x) = ( 1 + x * A(x)^2 * (1 + A(x)^(1/2)) )^2.
%F A371676 a(n) = 2 * Sum_{k=0..n} binomial(n,k) * binomial(4*n+k+2,n)/(4*n+k+2).
%o A371676 (PARI) a(n, r=2, t=4, u=1) = r*sum(k=0, n, binomial(n, k)*binomial(t*n+u*k+r, n)/(t*n+u*k+r));
%Y A371676 Cf. A006319, A032349, A371675. A371677, A371678.
%Y A371676 Cf. A260332.
%K A371676 nonn
%O A371676 0,2
%A A371676 _Seiichi Manyama_, Apr 02 2024