OFFSET
0,2
LINKS
Winston de Greef, Table of n, a(n) for n = 0..932
FORMULA
n*a(n) = 3 * ( (3*n-2)*a(n-1) + 3*(3*n-4)*a(n-2) + 3*(3*n-6)*a(n-3) + (3*n-8)*a(n-4) ) for n > 3.
a(n) = Sum_{k=0..n} (-9)^k * binomial(-1/3,k) * binomial(3*k,n-k).
a(n) = (-9)^n*binomial(-1/3, n)*hypergeom([(1-3*n)/4, (2-3*n)/4, 3*(1-n)/4, -3*n/4], [1/3-n, 2/3-n, 2/3-n], -2^8/3^5). - Stefano Spezia, Jul 11 2024
MATHEMATICA
a[n_]:=(-9)^n*Binomial[-1/3, n]HypergeometricPFQ[{(1-3*n)/4, (2-3*n)/4, 3*(1-n)/4, -3*n/4}, {1/3-n, 2/3-n, 2/3-n}, -2^8/3^5]; Array[a, 21, 0] (* Stefano Spezia, Jul 11 2024 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-9*x*(1+x)^3)^(1/3))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 26 2023
STATUS
approved