  We give explicit evaluations of the linear and non-linear Euler sums of
hyperharmonic numbers $h_{n}^{\left( r\right) }$ with reciprocal binomial
coefficients. These evaluations enable us to extend closed form formula of
Euler sums of hyperharmonic numbers to an arbitrary integer $r$. Moreover, we
reach at explicit formulas for the shifted Euler-type sums of harmonic and
hyperharmonic numbers. All the evaluations are provided in terms of the Riemann
zeta values, harmonic numbers and linear Euler sums.
