A372086 G.f. A(x) satisfies A(x) = 1/( 1 - 4*x*(1 + x)*A(x) )^(1/2).
1, 2, 12, 84, 664, 5624, 49928, 458480, 4318896, 41503168, 405267840, 4009684608, 40109536992, 404977089792, 4121810315584, 42243756499328, 435593319238144, 4515817056202496, 47040399766319360, 492117122988795392, 5168258741713256960
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, 4^k*binomial(3*k/2-1/2, k)*binomial(k, n-k)/(k+1));
Formula
a(n) = Sum_{k=0..n} 4^k * binomial(3*k/2-1/2,k) * binomial(k,n-k)/(k+1).