Conjecture no.12 A conjecture related to Brocard’s Problem

The equation n!!+1=k^2n+1 where n>0 has no integer solutions for all positive integers.

Here the double factorial indicates that the product of all even or odd integers =< n.

For example 8!! is equal to 2*4*6*8.

As always I welcome the readers to try proving or disproving this conjecture.

https://en.m.wikipedia.org/wiki/Brocard%27s_problem