A376568 Expansion of 1/(1 - 9*x*(1 + x))^(2/3).
1, 6, 51, 450, 4095, 37908, 354978, 3351348, 31833945, 303822090, 2910657321, 27970777926, 269484894081, 2602002636540, 25170322256010, 243876058527132, 2366251795228437, 22987502934573762, 223563791480714685, 2176402892261301990, 21206170582394740371
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, (-9)^k*binomial(-2/3, k)*binomial(k, n-k));
Formula
a(n) = 3*((3*n-1)*a(n-1) + (3*n-2)*a(n-2))/n for n > 1.
a(n) = Sum_{k=0..n} (-9)^k * binomial(-2/3,k) * binomial(k,n-k).
a(n) ~ (3 + sqrt(13))^(n + 2/3) * 3^n / (Gamma(2/3) * 13^(1/3) * n^(1/3) * 2^(n + 2/3)). - Vaclav Kotesovec, Oct 26 2024