Inverse of some matrix related to double zeta values of odd weight.

In this paper, we give a proof of a conjecture made by Zagier in [4] about the inverse of some matrix related to double zeta values of parity ( even , odd ) . As a result, we obtain a family of Bernoulli number identities. We further generalize this family to a more general setting involving binomial coefficients of negative arguments. [ABSTRACT FROM AUTHOR]