OFFSET
0,3
COMMENTS
In general, column k of A213027 is (for k > 1) asymptotic to a(n) ~ 3^(3*n+1/2) * (k-1)^(n+1) / (sqrt(Pi) * (2*k-3)^2 * 4^n * n^(3/2)). - Vaclav Kotesovec, Aug 31 2014
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*9^j for n>0, a(0) = 1.
Recurrence: 2*n*(2*n-1)*(13*n-15)*a(n) = (55159*n^3 - 95963*n^2 + 38478*n - 1080)*a(n-1) - 27000*(3*n-5)*(3*n-4)*(13*n-2)*a(n-2). - Vaclav Kotesovec, Aug 31 2014
a(n) ~ 3^(5*n+5/2) / (289 * sqrt(Pi) * 4^n * n^(3/2)). - Vaclav Kotesovec, Aug 31 2014
MAPLE
a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*9^j, j=0..n-1)/n):
seq(a(n), n=0..20);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 29 2012
STATUS
approved