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What will be the sequence generated by the generating function 4x/(1-x)^2?

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What will be the sequence generated by the generating function 4x/(1-x)^2?

(a) 12, 16, 20, 24,…

(b) 1, 3, 5, 7, 9,…

(c) 0, 4, 8, 12, 16, 20,…

(d) 0, 1, 1, 3, 5, 8, 13,…

This question was addressed to me during an internship interview.

The question is from Discrete Probability in portion Discrete Probability of Discrete Mathematics

1 Answer

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Right answer is (c) 0, 4, 8, 12, 16, 20,…

Easy explanation: The sequence should be 0, 4, 8, 12, 16, 20,…for the generating function 4x/(1-x)^2, when basic generating function: 1/(1-x).

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