A382920 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) / (1-x)^2 )^3.
1, 3, 21, 160, 1320, 11511, 104451, 976317, 9337182, 90937403, 898861308, 8994246132, 90932043400, 927452701605, 9531607969788, 98609173435172, 1026121044859890, 10733030463200814, 112783955395845926, 1190060614961391945, 12604133970419399208, 133945684546835994915
Offset: 0
Keywords
Programs
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PARI
a(n, r=3, s=2, t=4, u=0) = 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 + x*A(x)^(4/3) / (1-x)^2 )^3.
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).
G.f.: B(x)^3, where B(x) is the g.f. of A382916.