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 A378889 #12 Dec 10 2024 05:52:15
%S A378889 1,3,12,61,348,2127,13617,90132,611802,4235405,29788821,212255520,
%T A378889 1528928674,11115361491,81452537253,601004875689,4461440570523,
%U A378889 33295962947925,249673885001674,1880204670772221,14213624028779964,107823953314047139,820541644515512502
%N A378889 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(4/3)/(1 + x*A(x)^(1/3)) )^3.
%F A378889 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)/(1 + x*A(x)^(1/3)) )^3.
%F A378889 G.f. A(x) satisfies A(x) = 1 + x * A(x)^(1/3) * (1 + A(x)^(4/3) + A(x)^(5/3)).
%F A378889 G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A364758.
%F A378889 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 A378889 (PARI) a(n, r=3, s=-1, t=4, u=1) = 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 A378889 Cf. A371542, A378890, A378891.
%Y A378889 Cf. A364758.
%K A378889 nonn
%O A378889 0,2
%A A378889 _Seiichi Manyama_, Dec 10 2024