A383610 Expansion of 1/( (1-x^2) * (1-x^2-9*x)^2 )^(1/3).
1, 6, 46, 372, 3106, 26406, 227179, 1970952, 17206552, 150940848, 1329193288, 11741662152, 103992267826, 923052335316, 8208568670644, 73116321077784, 652195543067596, 5824848557238228, 52080340709333998, 466116121318516872, 4175438344430632696
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\2, (-9)^(n-2*k)*binomial(-2/3, n-2*k)*binomial(n-k, k));
Formula
a(n) = Sum_{k=0..floor(n/2)} (-9)^(n-2*k) * binomial(-2/3,n-2*k) * binomial(n-k,k).
a(n) ~ Gamma(1/3) * (9 + sqrt(85))^(n+1) / (Pi * 3^(1/6) * 85^(1/3) * n^(1/3) * 2^(n+2)). - Vaclav Kotesovec, May 03 2025