If the Maclaurin series for eue^ueu is ∑n=0∞unn!\sum_{n=0}^{\infty} \frac{u^n}{n!}∑n=0∞n!un, what is the Maclaurin series for ex2e^{x^2}ex2?
∑n=0∞x2nn!\sum_{n=0}^{\infty} \frac{x^{2n}}{n!}∑n=0∞n!x2n
∑n=0∞x2n(2n)!\sum_{n=0}^{\infty} \frac{x^{2n}}{(2n)!}∑n=0∞(2n)!x2n
∑n=0∞(2x)nn!\sum_{n=0}^{\infty} \frac{(2x)^n}{n!}∑n=0∞n!(2x)n
∑n=0∞xnn!⋅2n\sum_{n=0}^{\infty} \frac{x^n}{n! \cdot 2^n}∑n=0∞n!⋅2nxn