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 A378686 #12 Dec 04 2024 09:11:55
%S A378686 1,3,27,313,4122,58584,875897,13577139,216224616,3516601243,
%T A378686 58160887857,975211608399,16539799297342,283243124783136,
%U A378686 4890858070498203,85060240453556192,1488653675438168001,26197808077514204832,463311206395709908936,8229849868810254813378
%N A378686 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(7/3)/(1 - x*A(x)) )^3.
%F A378686 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^2/(1 - x*A(x)) )^3.
%F A378686 G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A378685.
%F A378686 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 A378686 (PARI) a(n, r=3, s=1, t=7, u=3) = 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 A378686 Cf. A108447, A371581.
%Y A378686 Cf. A349017, A369012.
%Y A378686 Cf. A378690, A378692, A378693.
%Y A378686 Cf. A378685.
%K A378686 nonn
%O A378686 0,2
%A A378686 _Seiichi Manyama_, Dec 04 2024