Looks like you can express each term as

a_n = (n!)^2 / (4n+1)(4n-1)(4n-3)…1

Now you can use the ratio test to see if the series converges
It seems to me test convergence need to take place

the numerator follows (N!)\^2

but the denominator has 2n-1  numbers multiplied which i don't know how it would lookk for the given series in equation
Σ from n=1 to inf of ((n!)^2 • Π from i=0 to 2n of 1/(2i+1))