A378691 G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 - x*A(x)).
1, 1, 7, 65, 699, 8192, 101538, 1309007, 17373825, 235820907, 3258327727, 45676003435, 648019627185, 9286982935406, 134247731827970, 1955128344950960, 28659409029300490, 422517375650417841, 6260750426764454787, 93191618760715641120, 1392823412892172416996
Offset: 0
Keywords
Programs
-
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));
Formula
G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^5/(1 - x*A(x))).
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).