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 A378691 #10 Dec 04 2024 09:11:13
%S A378691 1,1,7,65,699,8192,101538,1309007,17373825,235820907,3258327727,
%T A378691 45676003435,648019627185,9286982935406,134247731827970,
%U A378691 1955128344950960,28659409029300490,422517375650417841,6260750426764454787,93191618760715641120,1392823412892172416996
%N A378691 G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 - x*A(x)).
%F A378691 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^5/(1 - x*A(x))).
%F A378691 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 A378691 (PARI) a(n, r=1, s=1, t=6, u=1) = 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 A378691 Cf. A000108, A001003, A108447, A364747, A364748, A378692.
%K A378691 nonn
%O A378691 0,3
%A A378691 _Seiichi Manyama_, Dec 04 2024