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 A378890 #11 Dec 10 2024 06:14:02
%S A378890 1,3,15,97,711,5613,46552,399918,3527553,31761600,290721387,
%T A378890 2697131541,25304974597,239684681523,2288849098119,22012319667437,
%U A378890 213011739042714,2072597720747352,20264567643461700,198998140737895692,1961831436443431818,19409477239837165874
%N A378890 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(5/3)/(1 + x*A(x)^(2/3)) )^3.
%F A378890 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^(4/3)/(1 + x*A(x)^(2/3)) )^3.
%F A378890 G.f. A(x) satisfies A(x) = 1 + x * A(x)^(2/3) * (1 + A(x)^(4/3) + A(x)^(5/3)).
%F A378890 G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A365225.
%F A378890 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(s*k,n-k)/(t*k+u*(n-k)+r).
%o A378890 (PARI) a(n, r=3, s=-1, t=5, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
%Y A378890 Cf. A371542, A378889, A378891.
%Y A378890 Cf. A365225.
%K A378890 nonn
%O A378890 0,2
%A A378890 _Seiichi Manyama_, Dec 10 2024