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Reference request: Gessel interview's generating function identities

In this interview, Ira Gessel mentions the following results: Result 1: Let $B_n$ denote the $n^{\text{th}}$ Bernoulli number. Define the series $$B(x) = \sum_{n=2}^{\infty} \frac{B_nx^{n-1}}{n(n-1)}.$...