20 persons are invited for a party. The different number of ways in which they can be seated on a circular table with two particular persons seated on either side of the host is

Two perticular persons can sit either side of the host in 2 ways

The remaining 18 guests and this group of having host and two perticualr persons, total 19 can arrange around a table in $18!$ ways

Therefore, the number of required arrangements is $\boxed{2\left(18!\right)}$