Weighted sum formulas from shuffle products of multiples of Riemann zeta values

On three general forms of multiple zeta(-star) values

“…This formula is a special case in [22,Theorem 4]. For the case n = 1 in Eq (1.8), we have There is another expression given by the second author and Yang [11]: The inner summation of the above sum is given by Zagier [21]:…”