  In this paper we show that there is a cut-off in the Khovanov homology of
$(2k,2kn)$-torus links, namely that the maximal homological degree of non-zero
homology group of $(2k,2kn)$-torus link is $2k^2n$. Furthermore, we calculate
explicitely the homology groups in homological degree $2k^2n$ and prove that it
coincides with the centre of the ring $H^k$ of crossingless matchings,
introduced by M. Khovanov in \cite{tan}. Also we give an explicit formula for
the ranks of the homology groups of $(3,n)$-torus knots for every $n\in\N$.
