A377260 Expansion of 1/(1 - 9*x*(1 + x))^(4/3).
1, 12, 138, 1512, 16191, 170856, 1785042, 18514548, 190978047, 1961435736, 20074741596, 204870399552, 2085761241018, 21191569851312, 214930928188116, 2176565295933000, 22012171108148025, 222351327936731700, 2243667436429422150, 22618648367553735000, 227826739721910301245
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, (-9)^k*binomial(-4/3, 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(-4/3,k) * binomial(k,n-k).
a(n) ~ n^(1/3) * 3^(n+1) * (3 + sqrt(13))^(n + 4/3) / (13^(2/3) * Gamma(1/3) * 2^(n + 4/3)). - Vaclav Kotesovec, May 03 2025