A378690 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(7/2)/(1 - x*A(x)) )^2.
1, 2, 17, 190, 2438, 33938, 498413, 7602010, 119261202, 1912171310, 31194947785, 516153663072, 8641160417191, 146105874059670, 2491396820758004, 42795782630083868, 739842609794223330, 12862556429464405500, 224744883747568868574, 3944534317072930309360
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Keywords
Programs
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PARI
a(n, r=2, 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));
Formula
G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^3/(1 - x*A(x)) )^2.
G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A378688.
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).