  We prove that the operad of mock partially associative $n$-ary algebras is
not Koszul, as conjectured by the second and the third author in 2009, and
utilise the Zeilberger's algorithm for hypergeometric summation to demonstrate
that non-Koszulness of that operad cannot be established by hunting for
negative coefficients in the inverse of its Poincar\'e series.
