OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..300
FORMULA
a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*3^j for n>0, a(0) = 1.
a(n) ~ 3^(4*n+3/2) / (25*sqrt(Pi)*n^(3/2)*4^n). - Vaclav Kotesovec, Jul 16 2014
MAPLE
a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*3^j, j=0..n-1)/n):
seq(a(n), n=0..20);
# second Maple program:
a:= proc(n) option remember; `if`(n<3, [1, 1, 10][n+1],
((2359*n^3 -5063*n^2 +2898*n -360)*a(n-1)
-576*(3*n-5)*(7*n-2)*(3*n-4)*a(n-2))/
(2*(2*n-1)*(7*n-9)*n))
end:
seq(a(n), n=0..30);
MATHEMATICA
a[n_] := If[n == 0, 1, Sum[Binomial[3n, j] (n - j) 3^j, {j, 0, n - 1}]/n];
a /@ Range[0, 20] (* Jean-François Alcover, Dec 18 2020, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 29 2012
STATUS
approved