A382894 G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^3 * A(x) )^2.
1, 2, 13, 78, 520, 3664, 26859, 202808, 1566693, 12323982, 98381841, 795023284, 6490951398, 53462144788, 443683640945, 3706539244272, 31144893093298, 263052053436600, 2231992880546400, 19016760502183968, 162629329186013523, 1395500273826639540
Offset: 0
Keywords
Programs
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PARI
a(n, r=2, s=3, t=3, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
Formula
G.f. A(x) satisfies A(x) = ( 1 + x * (1+x)^3 * A(x)^(3/2) )^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(s*k,n-k)/(t*k+u*(n-k)+r).
G.f.: B(x)^2, where B(x) is the g.f. of A366200.