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A361844
Expansion of 1/(1 - 9*x*(1-x)^2)^(1/3).
7
1, 3, 12, 57, 297, 1629, 9216, 53217, 311796, 1846818, 11032416, 66356712, 401364531, 2439135585, 14882263002, 91116281565, 559528781697, 3445002647847, 21260140172244, 131474746842345, 814564464082263, 5055177167348463, 31420067723814780
OFFSET
0,2
LINKS
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
Column k=2 of A361840.
Sequence in context: A328295 A194089 A178807 * A047891 A166991 A276366
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 26 2023
STATUS
approved