How to write multiplication of series of numbers in factorial form?

Question

I want to write

$$1 \times 2 \times 3 \times \dotsb \times 1 \times 5 \times 9 \times 13 \times \dotsb$$

in factorial form, but I don't know how?

Answer 1

You could use multifactorial notation:

$1 \times 2 \times 3 \times \dotsb \times n \times 1 \times 5 \times 9 \times \dotsb \times (4m+1) = n! \times (4m+1)!!!!$