Let n>1. Recall that an n-ary totally associative algebra has one degree 0 n-ary multiplication m that is totally associative in the sense that the result of iterated multiplication is independent on the association. It is known that the corresponding operad tAss is Koszul for all n>1. Likewise, an n-ary totally anti-associative algebra has one n-ary totally associative multiplication m, which is now assumed to be of degree 1. In a joint work with E. Remm we proved that the operad anti-tAss for anti-associative n-ary algebras is not Koszul for n<8 and conjectured it is non-Koszul for an arbitrary n. We then performed several numerical experiments with the generating series of anti-tAss which, very surprisingly, seem to indicate rather that anti-tAss is Koszul for n>7, and suggest several other interesting phenomena. The talk will be devoted to them.