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 A378693 #9 Dec 04 2024 09:10:39
%S A378693 1,6,63,806,11445,173388,2745470,44891118,752141682,12845874594,
%T A378693 222813745704,3914269052736,69501455945987,1245309605501088,
%U A378693 22488056019050124,408861223600687710,7478056231521533658,137496627558561863460,2540015518588821201453
%N A378693 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(7/6)/(1 - x*A(x)) )^6.
%F A378693 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)/(1 - x*A(x)) )^6.
%F A378693 G.f.: A(x) = B(x)^6 where B(x) is the g.f. of A378694.
%F A378693 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 A378693 (PARI) a(n, r=6, s=1, t=7, u=6) = 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 A378693 Cf. A378686, A378690, A378692.
%Y A378693 Cf. A378694.
%K A378693 nonn
%O A378693 0,2
%A A378693 _Seiichi Manyama_, Dec 04 2024