The series given is:

In general, the -th term of the series, denoted as , takes the form:

To simplify , we write it in terms of factorials:

Thus, the series can be expressed as:

This breaks into two parts:

Each part is a well-known series. Specifically:

, starting from the term where , which aligns with the expansion of e.
, for the terms starting where .

Consequently, the sum of the entire series is:

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