A382917 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^3 / (1-x)^3 ).
1, 1, 7, 52, 432, 3878, 36694, 360498, 3642534, 37613947, 395204413, 4211469308, 45409525116, 494500127617, 5430864937915, 60083846523038, 669005596426438, 7491245872785003, 84305386452532885, 953020276395635246, 10816782722212619970, 123218274878407738497
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Keywords
Programs
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PARI
a(n, r=1, s=3, 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 / (1-x)^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).