OFFSET
0,2
LINKS
Winston de Greef, Table of n, a(n) for n = 0..932
FORMULA
a(n) = Sum_{k=0..n} (-9)^k * binomial(-1/3,k) * binomial(n+2*k-1,n-k).
a(0) = 1; a(n) = (3/n) * Sum_{k=0..n-1} (n+2*k) * binomial(n+1-k,2) * a(k).
a(n) = 3*n*(1 + n)*hypergeom([1-n, 1+n/2, (3+n)/2], [5/3, 2], -4/3)/2 for n > 0. - Stefano Spezia, May 02 2024
MATHEMATICA
a[0]=1; a[n_]:=3*n*(1 + n)*HypergeometricPFQ[{1-n, 1+n/2, (3+n)/2}, {5/3, 2}, -4/3]/2; Array[a, 21, 0] (* Stefano Spezia, May 02 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 28 2023
STATUS
approved