OFFSET
0,3
LINKS
Winston de Greef, Table of n, a(n) for n = 0..1328
FORMULA
a(n) = Sum_{k=0..floor(n/2)} (3*k)!/k!^3 * binomial(k,n-2*k).
From Vaclav Kotesovec, Mar 23 2023: (Start)
Recurrence: (n-1)*n^2*a(n) = -(n-1)^2*n*a(n-1) + 3*(n-1)*(3*n - 4)*(3*n - 2)*a(n-2) + 18*(n-2)*(3*n^2 - 6*n + 1)*a(n-3) + 27*(n-3)*(n-2)*n*a(n-4).
a(n) ~ sqrt(3) * (6*cos(Pi/9))^n / (2*Pi*n). (End)
MATHEMATICA
Table[Sum[(3*k)!/k!^3 * Binomial[k, n-2*k], {k, 0, n/2}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 23 2023 *)
PROG
(PARI) a(n) = sum(k=0, n\2, (3*k)!/k!^3*binomial(k, n-2*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 22 2023
STATUS
approved