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 A378828 #40 Dec 10 2024 05:53:37
%S A378828 1,3,12,61,354,2220,14649,100218,704373,5055383,36895221,272975652,
%T A378828 2042782905,15434838759,117588475377,902259691317,6966487019220,
%U A378828 54086849181609,421986564474946,3306818224272945,26015737668878523,205405810986995869,1627042895593132485
%N A378828 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(2/3)/(1 - x*A(x)^(4/3)) )^3.
%F A378828 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^(1/3)/(1 - x*A(x)^(4/3)) )^3.
%F A378828 G.f. A(x) satisfies A(x) = 1 + x * A(x)^(2/3) * (1 + A(x)^(1/3) + A(x)^(5/3)).
%F A378828 G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A364739.
%F A378828 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).
%o A378828 (PARI) a(n, r=3, s=1, t=2, u=4) = 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));
%Y A378828 Cf. A349017, A378801, A378882.
%Y A378828 Cf. A364739, A378889.
%K A378828 nonn
%O A378828 0,2
%A A378828 _Seiichi Manyama_, Dec 09 2024