Sequence and Series: JEE Main 2023 Mathematics question

Let \sum_\limits{n=0}^{\infty} \frac{\mathrm{n}^{3}((2 \mathrm{n}) !)+(2 \mathrm{n}-1)(\mathrm{n} !)}{(\mathrm{n} !)((2 \mathrm{n}) !)}=\mathrm{ae}+\frac{\mathrm{b}}{\mathrm{e}}+\mathrm{c}, where $\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbb{Z}$ and e=\sum_\limits{\mathrm{n}=0}^{\infty} \frac{1}{\mathrm{n} !} Then $\mathrm{a}^{2}-\mathrm{b}+\mathrm{c}$ is equal to ____________.