A378693 - OEIS

%I #9 Dec 04 2024 09:10:39

%S 1,6,63,806,11445,173388,2745470,44891118,752141682,12845874594,

%T 222813745704,3914269052736,69501455945987,1245309605501088,

%U 22488056019050124,408861223600687710,7478056231521533658,137496627558561863460,2540015518588821201453

%N G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(7/6)/(1 - x*A(x)) )^6.

%F G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)/(1 - x*A(x)) )^6.

%F G.f.: A(x) = B(x)^6 where B(x) is the g.f. of A378694.

%F 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 (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 Cf. A378686, A378690, A378692.

%Y Cf. A378694.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 04 2024