A382916 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^3 / (1-x)^2 ).
1, 1, 6, 41, 316, 2636, 23192, 211926, 1992032, 19138016, 187091252, 1855104372, 18612229836, 188601299149, 1927443803738, 19843158497163, 205602235405524, 2142401581747657, 22436439910929038, 236023405797017891, 2492914862240934612, 26426682321857813417
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Keywords
Programs
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PARI
a(n, r=1, 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 / (1-x)^2.
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).