Build a generating function for a_r, the number of integer solutions to the equation e1 + e2 + + e3 = r; 2 lessthanorequlto e_i lessthanorequlto 8, e1 is even, e2 is odd.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: