Rational approximations to values of Bell polynomials at points involving Euler's constant and zeta values

In this paper, we present new explicit simultaneous rational approximations converging sub-exponentially to the values of Bell polynomials at the points of the form $(\gamma, 1! (2a+1)\zeta(2), 2!\zeta(3),..., (m-1)!(a+1+(-1)^ma)\zeta(m)),$ $m=1,2,...,a,$ $a\in{\mathbb N}.$