Recurring series term and sum

Find the $n^{e x t t h}$ term and the sum to $n$ terms of the series $2 + 7x + 25x^2 + 91x^3 +
otdots$.

~15 minAnswer checked instantlyrecurring seriesgenerating functionsummation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXIV. Recurring Series, Examples XXIV, No. 8

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).