OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} (3*k)!/k!^3 * binomial(k,n-k).
a(n) ~ sqrt(3) * ((27 + 3*sqrt(93))/2)^n / (2*Pi*n). - Vaclav Kotesovec, Mar 23 2023
MATHEMATICA
Table[Sum[(3*k)!/k!^3 * Binomial[k, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 23 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, (3*k)!/k!^3*binomial(k, n-k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 22 2023
STATUS
approved