A361841 - OEIS

%I #19 Mar 30 2023 09:14:59

%S 1,3,24,201,1809,16893,161676,1574289,15527052,154662930,1552725504,

%T 15688410264,159355067283,1625899880673,16652520666414,

%U 171119405299005,1763475423260049,18219685282559559,188664151412242368,1957539823296458841,20347733657193596127

%N Expansion of 1/(1 - 9*x*(1+x)^2)^(1/3).

%H Winston de Greef, <a href="/A361841/b361841.txt">Table of n, a(n) for n = 0..966</a>

%F n*a(n) = 3 * ( (3*n-2)*a(n-1) + 2*(3*n-4)*a(n-2) + (3*n-6)*a(n-3) ) for n > 2.

%F a(n) = Sum_{k=0..n} (-9)^k * binomial(-1/3,k) * binomial(2*k,n-k).

%F a(n) = (-9)^n*binomial(-1/3, n)*hypergeom([1/3 - n*2/3, 2/3 - n*2/3, -n*2/3], [1/2 - n, 2/3 - n], -3/4). - _Peter Luschny_, Mar 27 2023

%p A361841 := n -> (-9)^n*binomial(-1/3, n)*hypergeom([1/3 - n*2/3, 2/3 - n*2/3, -n*2/3], [1/2 - n, 2/3 - n], -3/4):

%p seq(simplify(A361841(n)), n = 0..20); # _Peter Luschny_, Mar 27 2023

%o (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-9*x*(1+x)^2)^(1/3))

%Y Column k=2 of A361839.

%Y Cf. A002478, A137635, A361844.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 26 2023