I have a problem in which I need to solve for a number of sequences using exponential generating functions. I understand how finding the coefficients of ordinary generating functions work, however, I cannot seem to wrap my head around how to find the coefficients using exponential generating functions.
I was given the following problem to solve:
How many 10-letter words are there in which each of the letters e, n, r, s occur at most once?
I produced the following generationg function.
$(x^0+x^1)^4 (x^0 + x^1 + x^2/2! + x^3/3! + \cdots)^{26-4}$
which simplifies to
$(1+x)^4 e^{22x}$
However now I am completely lost on how to solve for the coefficients. Could somebody explain to me how to do this? Thanks