A377234 - OEIS

%I #11 Oct 21 2024 05:06:05

%S 1,12,138,1524,16455,175152,1846164,19320456,201093843,2084105820,

%T 21524823858,221678089716,2277558628869,23352604052952,

%U 239024756624520,2442818071519104,24932208295715538,254166614639215032,2588333499216072516,26333774228774140680,267693203735009601870

%N Expansion of 1/(1 - 9*x/(1-x))^(4/3).

%F a(0) = 1; a(n) = 3 * Sum_{k=0..n-1} (4-k/n) * a(k).

%F a(n) = ((11*n+1)*a(n-1) - 10*(n-2)*a(n-2))/n for n > 1.

%F a(n) = Sum_{k=0..n} (-9)^k * binomial(-4/3,k) * binomial(n-1,n-k).

%F a(n) ~ 3^(11/3) * 10^(n - 4/3) * n^(1/3) / Gamma(1/3). - _Vaclav Kotesovec_, Oct 21 2024

%o (PARI) a(n) = sum(k=0, n, (-9)^k*binomial(-4/3, k)*binomial(n-1, n-k));

%Y Cf. A052268, A361375, A377233, A377235.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 21 2024