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

What is the sequence depicted by the generating series 4 + 15x^2 + 10x

1.	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» 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,…

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