A372105 G.f. A(x) satisfies A(x) = 1/( 1 - 9*x*A(x)/(1-x) )^(1/3).
1, 3, 30, 372, 5187, 77682, 1220421, 19842492, 331047138, 5635390827, 97491744102, 1709067567387, 30293505154362, 542010120629052, 9775907758416999, 177556754470826046, 3244682279388126576, 59614554914471797482, 1100573677912355195313
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, 9^k*binomial(4*k/3-2/3, k)*binomial(n-1, n-k)/(k+1));
Formula
a(n) = Sum_{k=0..n} 9^k * binomial(4*k/3-2/3,k) * binomial(n-1,n-k)/(k+1).