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What is the generating function for the generating sequence A = 1, 9, 25, 49,…?

What is the generating function for the generating sequence A = 1, 9, 25, 49,…? Correct Answer (1-A)-1/x

The generating function for the sequence A. Using differencing: A = 1 + 9x + 25x2 + 49x3 + ⋯(1) −xA = 0 + x + 9x2 + 25x3 + 49x4 + ⋯(2) (1−x)A = 1 + 8x + 16x2 + 24x3 +⋯. Since 8x + 16x2 + 24x3 + ⋯ = (1-x)A-1 ⇒ 8 + 16x + 24x2 +…= (1-A)-1/x.

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