Conjecture no. 40 On super double factorials

The equation n!!(n-1)!!(n-2)!!(n-k)! is equal to y factorial finitely often.

Some explicit examples are 5!!(4!!)(3!!)(2!!)(1!)= 6! , 3!!(2!!)(1!!)=3! , and 7!(6!!)(5!!)(4!!)(3!!)(2!!)(1!!)=10!

Here the double factorial indicates the product of all odd or even integers less than or equal to that integer.

For example, 5!!= 5*3*1 because 5, 3, and 1 are all the odd integers less than or equal to five.

As always I welcome the readers to prove or disprove this conjecture.

Thank you,

Nunghead