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A361841
Expansion of 1/(1 - 9*x*(1+x)^2)^(1/3).
4
1, 3, 24, 201, 1809, 16893, 161676, 1574289, 15527052, 154662930, 1552725504, 15688410264, 159355067283, 1625899880673, 16652520666414, 171119405299005, 1763475423260049, 18219685282559559, 188664151412242368, 1957539823296458841, 20347733657193596127
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) = 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
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):
seq(simplify(A361841(n)), n = 0..20); # 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 A361839.
Sequence in context: A063979 A308354 A370375 * A361880 A073978 A278991
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 26 2023
STATUS
approved