How many flops for Exponential Approximation?

[BlueChinchillaEatingDorito]

I'm trying to figure out the number of flops that are required to do this computation and I need some help figuring out the representation for the A^k and 1/k! terms

For A^k, where A is a n x n matrix, I know there are 2n^2 - n flops when doing matrix multiplications, but how would I account for k as it increases for each term?

Same with 1/k!. I know there are k-1 multiplications when calculating the factorial. But how would I account for the increasing value of n over k terms?