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 A378685 #12 Dec 04 2024 09:12:14
%S A378685 1,1,8,88,1126,15716,232069,3564835,56382489,912031280,15018257510,
%T A378685 250913307393,4242722219425,72470224174650,1248608968982903,
%U A378685 21673752440979879,378677335852165297,6654158090059397480,117523324766568499072,2085095374834405245007
%N A378685 G.f. A(x) satisfies A(x) = 1 + x*A(x)^7/(1 - x*A(x)^3).
%F A378685 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^6/(1 - x*A(x)^3)).
%F A378685 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 A378685 (PARI) a(n, r=1, 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 A378685 Cf. A243659, A300048.
%Y A378685 Cf. A108447, A365192.
%Y A378685 Cf. A378686.
%K A378685 nonn
%O A378685 0,3
%A A378685 _Seiichi Manyama_, Dec 04 2024