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- W2793208656 abstract "The tangent number T 2 n + 1 is equal to the number of increasing labelled complete binary trees with 2 n + 1 vertices. This combinatorial interpretation immediately proves that T 2 n + 1 is divisible by 2 n . However, a stronger divisibility property is known in the studies of Bernoulli and Genocchi numbers, namely, the divisibility of ( n + 1 ) T 2 n + 1 by 2 2 n . The traditional proofs of this fact need significant calculations. In the present paper, we provide a combinatorial proof of the latter divisibility by using the hook length formula for trees. Furthermore, our method is extended to k -ary trees, leading to a new generalization of the Genocchi numbers." @default.
- W2793208656 created "2018-03-29" @default.
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- W2793208656 date "2018-06-01" @default.
- W2793208656 modified "2023-09-30" @default.
- W2793208656 title "Combinatorial proofs of some properties of tangent and Genocchi numbers" @default.
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- W2793208656 doi "https://doi.org/10.1016/j.ejc.2018.02.041" @default.
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