Euler-type sums involving odd harmonic numbers and binomial coefficients

In this paper, by iterated integral expression of multiple t-polylogarithm function, we establish some expressions of series involving multiple t-harmonic sums in terms of coloured multiple zeta values. Using these expressions and the stuffle relations, we discuss the evaluations of some Euler-type sums involving odd harmonic numbers and binomial coefficients, such as Todd,k(q;r):=∑n=1∞hn−1(k1)⋯hn−1(kp)(2n−1)q(n+rr),Tevev,k(q;r):=∑n=1∞hn(k1)⋯hn(kp)nq(n+rr),Todd,k(q;r):=∑n=1∞hn−1(k)(2n−1)q∏i=1b(n+riri),Teven,k(q;r):=∑n=1∞hn(k)nq∏i=1b(n+riri),Todd,k1,k2(q;r):=∑n=1∞hn−1(k1)hn−1(k2)(2n−1)q∏i=1b(n+riri),Teven,k1,k2(q;r):=∑n=1∞hn(k1)hn(k2)nq∏i=1b(n+riri),and some other forms. We present some explicit evaluations as examples. It can be found that this work gives a unified approach to such sums, and generalizes many known results in the literature.