OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
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.
a(n) = (-1)^n * Sum_{k=0..n} 9^k * binomial(-1/3,k) * binomial(2*k,n-k).
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
MAPLE
A361844 := 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):
seq(simplify(A361844(n)), n = 0..22); # Peter Luschny, Mar 27 2023
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-9*x*(1-x)^2)^(1/3))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 26 2023
STATUS
approved