From sum to sum

Algebra Level 3

If

1+3x+5x2+7x3+9x4+=91,\large 1 + \frac{3}{x} + \frac{5}{x^2} + \frac{7}{x^3} + \frac{9}{x^4} +\ldots = 91,

then evaluate

1+4x+9x2+16x3+25x4+\large 1 + \frac{4}{x} + \frac{9}{x^2} + \frac{16}{x^3} + \frac{25}{x^4} +\ldots

×

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