It is shown that the "résultat " can be derived by simple traditional methods of classical analysis dealing with hypergeometric series (see CalculEmery pdf). Further extensions can also be obtained, such as a t-extension (see tCalculEmery pdf), a q-extension (see qCalculEmery pdf), and even a tq-extension (see tqCalculEmery). Finally, it is shown (see RandomPermutations pdf) that the so-called first fundamental transformation provides a natural combinatorial link between statistics involving cycle lengths of random permutations and statistics dealing with runs on Bernoulli sequences.
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