1 research outputs found
Combinatorial proofs of some properties of tangent and Genocchi numbers
The tangent number is equal to the number of increasing labelled
complete binary trees with vertices. This combinatorial interpretation
immediately proves that is divisible by . However, a stronger
divisibility property is known in the studies of Bernoulli and Genocchi
numbers, namely, the divisibility of by . 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 -ary
trees, leading to a new generalization of the Genocchi numbers