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A361895
Expansion of 1/(1 - 9*x/(1 - x)^3)^(1/3).
5
1, 3, 27, 252, 2487, 25434, 266364, 2837082, 30601233, 333302931, 3658565127, 40413860334, 448778693844, 5005642415907, 56044616215041, 629552293867800, 7092072533703567, 80095810435943526, 906605837653876254, 10282430320166723448, 116829834042508121682
OFFSET
0,2
LINKS
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))
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 28 2023
STATUS
approved