A378688 - OEIS

%I #8 Dec 04 2024 09:11:43

%S 1,1,8,87,1100,15173,221449,3362472,52571486,840658030,13685005046,

%T 226034078091,3778561589470,63808500324629,1086892630726300,

%U 18652582726212792,322197108441548095,5597514211552503858,97741241871353705160,1714482398765781043424

%N G.f. A(x) satisfies A(x) = 1 + x*A(x)^7/(1 - x*A(x)^2).

%F G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^6/(1 - x*A(x)^2)).

%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=1, s=1, t=7, u=2) = 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. A378690.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Dec 04 2024