Some weighted sum identities for double zeta values (Q327276)

The authors find some new weighted sum identities with respect to depth two multiple zeta values. More concretely, they give explicit expression, among others, for the sums \[ \sum_{k=2}^{s-1}(-1)^kk\zeta(k,s-k), \quad \sum_{k=1}^{s-1}k\zeta(2k,2s-2k), \quad \sum_{k=1}^{s-1}k^2\zeta(2k,2s-2k) \] in terms of harmonic numbers, zeta and double zeta values.