PASCAL’S TRIANGLE, SIDI POLYNOMIALS, AND POWERS OF e

In 2012, the author discovered that the base of the natural logarithm, e, can be derived by operating on the products of the rows of Pascal’s triangle. The unexpected result raised the question as to what other sequences through Pascal’s triangle might be connected to e. Employing a property of Sidi polynomials related to the factorial function, we prove that there are an infinite number of such sequences whose growth rates are asymptotic to powers of e.