Question

What is the sequence depicted by the generating series 4 + 15x^2 + 10x^3 + 25x^5 + 16x^6+⋯?

(a) 10, 4, 0, 16, 25, …

(b) 0, 4, 15, 10, 16, 25,…

(c) 4, 0, 15, 10, 25, 16,…

(d) 4, 10, 15, 25,…

The question was asked during an interview.

I would like to ask this question from Discrete Probability in section Discrete Probability of Discrete Mathematics

Answer 1

Correct answer is (c) 4, 0, 15, 10, 25, 16,…

For explanation I would say: Consider the coefficients of each x^n term. So a0=4, since the coefficient of x0 is 4 (x0=1 so this is the constant term). Since 15 is the coefficient of x^2, so 15 is the term a2 of the sequence. To find a1 check the coefficient of x1 which in this case is 0. So a1=0. Continuing with these we have a2=15, a3=10, a4=25, and a5=16. So we have the sequence 4, 0, 15, 10, 25, 16,…