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%I #11 Dec 04 2024 09:10:52
%S 1,1,8,86,1075,14667,211799,3182454,49243854,779379652,12558073022,
%T 205312307834,3397359326116,56790504859929,957574385205771,
%U 16267419813629731,278162968238908681,4783813617177604232,82691541747420586716,1435895455224032519430,25035634270828781060188
%N G.f. A(x) satisfies A(x) = 1 + x*A(x)^7/(1 - x*A(x)).
%F G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^6/(1 - x*A(x))).
%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=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 Cf. A000108, A001003, A108447, A364747, A364748, A378691.
%Y Cf. A378686, A378690, A378693.
%Y Cf. A378685, A378688, A378694.
%K nonn,new
%O 0,3
%A _Seiichi Manyama_, Dec 04 2024