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 A364747 #20 Dec 05 2024 07:27:24
%S A364747 1,1,5,32,234,1854,15490,134380,1198944,10931761,101412677,954155059,
%T A364747 9083120975,87326765375,846709605539,8269910074087,81291388929027,
%U A364747 803592049667495,7983612883739843,79671910265120574,798283229227457304,8027625597750959053
%N A364747 G.f. A(x) satisfies A(x) = 1 + x*A(x)^4 / (1 - x*A(x)).
%H A364747 Seiichi Manyama, <a href="/A364747/b364747.txt">Table of n, a(n) for n = 0..972</a>
%F A364747 a(n) = (1/n) * Sum_{k=0..n-1} binomial(n,k) * binomial(4*n-3*k,n-1-k) for n > 0.
%F A364747 From _Seiichi Manyama_, Dec 05 2024: (Start)
%F A364747 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^3/(1 - x*A(x))).
%F A364747 If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r). (End)
%o A364747 (PARI) a(n) = if(n==0, 1, sum(k=0, n-1, binomial(n, k)*binomial(4*n-3*k, n-1-k))/n);
%o A364747 (PARI) a(n, r=1, s=1, t=4, u=1) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r)); \\ _Seiichi Manyama_, Dec 05 2024
%Y A364747 Cf. A000108, A001003, A108447, A364748, A378691, A378692.
%Y A364747 Cf. A002294, A243659, A364765, A364792.
%K A364747 nonn
%O A364747 0,3
%A A364747 _Seiichi Manyama_, Aug 05 2023