International Journal of Number Theory
Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper, we prove a family of identities involving Bernoulli numbers and apply them to obtain infinitely many weighted sum formulas for double zeta values and triple zeta values where the weight coefficients are given by symmetric polynomials. We give a general conjecture in arbitrary depth at the end of the paper.
Guo, Li, Peng Lei, Jianqiang Zhao.
"Families of Weighted Sum Formulas for Multiple Zeta Values."
International Journal of Number Theory, 11 (3): 997.
doi: 10.1142/S1793042115500530 source: http://arxiv.org/abs/1401.6461