A377234 Expansion of 1/(1 - 9*x/(1-x))^(4/3).
1, 12, 138, 1524, 16455, 175152, 1846164, 19320456, 201093843, 2084105820, 21524823858, 221678089716, 2277558628869, 23352604052952, 239024756624520, 2442818071519104, 24932208295715538, 254166614639215032, 2588333499216072516, 26333774228774140680, 267693203735009601870
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, (-9)^k*binomial(-4/3, k)*binomial(n-1, n-k));
Formula
a(0) = 1; a(n) = 3 * Sum_{k=0..n-1} (4-k/n) * a(k).
a(n) = ((11*n+1)*a(n-1) - 10*(n-2)*a(n-2))/n for n > 1.
a(n) = Sum_{k=0..n} (-9)^k * binomial(-4/3,k) * binomial(n-1,n-k).
a(n) ~ 3^(11/3) * 10^(n - 4/3) * n^(1/3) / Gamma(1/3). - Vaclav Kotesovec, Oct 21 2024
a(n) = 12*hypergeom([7/3, 1-n], [2], -9) for n > 0. - Stefano Spezia, May 04 2025