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 A371678 #15 Jan 10 2025 12:06:27
%S A371678 1,4,56,1068,23504,561972,14183880,371911132,10031990560,276589937892,
%T A371678 7759696110808,220805824681740,6357540660485616,184876232243020564,
%U A371678 5422016433851400552,160187931368799105468,4763038761416835095616,142426926824923660491716
%N A371678 G.f. satisfies A(x) = 1 + x * A(x)^3 * (1 + A(x)^(1/2))^2.
%H A371678 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 A371678 G.f. satisfies A(x) = ( 1 + x * A(x)^3 * (1 + A(x)^(1/2)) )^2.
%F A371678 G.f.: B(x)^2 where B(x) is the g.f. of A371700.
%F A371678 a(n) = 2 * Sum_{k=0..n} binomial(n,k) * binomial(6*n+k+2,n)/(6*n+k+2).
%o A371678 (PARI) a(n, r=2, t=6, u=1) = r*sum(k=0, n, binomial(n, k)*binomial(t*n+u*k+r, n)/(t*n+u*k+r));
%Y A371678 Cf. A006319, A032349, A371675. A371676, A371677.
%Y A371678 Cf. A371700.
%K A371678 nonn
%O A371678 0,2
%A A371678 _Seiichi Manyama_, Apr 02 2024