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What is the sequence depicted by the generating series 4 + 15x2 + 10x3 + 25x5 + 16x6+⋯?

What is the sequence depicted by the generating series 4 + 15x2 + 10x3 + 25x5 + 16x6+⋯? Correct Answer 4, 0, 15, 10, 25, 16,…

Consider the coefficients of each xn 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 x2, 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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