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According to Maple your sum is:
$$ 1/2\,{\frac {{x}^{2}{3F1(1,2,-n;\,3;\,-x)}}{n!}} $$$$ \,{\frac {{x}^{2}{_3F_1(1,2,-n;\,3;\,-x)}}{2n!}} $$
1/2/n!*x^2*hypergeom([1, 2, -n],[3],-x)
$$ 1/2\,{\frac {{x}^{2}{3F1(1,2,-n;\,3;\,-x)}}{n!}} $$
$$ \,{\frac {{x}^{2}{_3F_1(1,2,-n;\,3;\,-x)}}{2n!}} $$
