There are some easy products that can be written in closed form in terms of factorials:
$ 2 \times 4 \times 6 \times ... 2n = n! \times 2^n$
$ 1 \times 3 \times 5 \times ... (2n-1) = {{(2n)!} \over {n! \times 2^n}}$
$ 3 \times 6 \times 9 \times ... 3n = n! \times 3^n$
But what about these?
$ f_2(n) = 2 \times 5 \times 8 \times ... (3n+2)$
$ f_1(n) = 1 \times 4 \times 7 \times ... (3n+1)$
Wolfram Alpha gives some expressions for partial products in terms of gamma functions, but is there any way to use factorials instead?