  We study the time evolution of Renyi entanglement entropy for locally excited
states in two dimensional large central charge CFTs. It generically shows a
logarithmical growth and we compute the coefficient of $\log t$ term. Our
analysis covers the entire parameter regions with respect to the replica number
$n$ and the conformal dimension $h_O$ of the primary operator which creates the
excitation. We numerically analyse relevant vacuum conformal blocks by using
Zamolodchikov's recursion relation. We find that the behavior of the conformal
blocks in two dimensional CFTs with a central charge $c$, drastically changes
when the dimensions of external primary states reach the value $c/32$. In
particular, when $h_O\geq c/32$ and $n\geq 2$, we find a new universal formula
$\Delta S^{(n)}_A\simeq \frac{nc}{24(n-1)}\log t$. Our numerical results also
confirm existing analytical results using the HHLL approximation.
