Re using an auto incremented primary key

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SQL-Server

SQL-Server-2008

Suppose i have a table called customer which is as follows

create table customer(
customerid int identity(1,1) primary key,
customername varchar(50),
emailid varchar(30) unique,
address varchar(max),
stateid int foreign key references state(stateid)
)

now i have a table called deletecustom which is like

create table deletecustom(
deletionid int identity(1,1) primary key,
customerid int 
)

i need to delete the entry in the customer table for the value inserted in the deletecustom table
so i use a trigger like

create trigger deletecustomer on deletecustom
for insert
as
declare @cid int;
select @cid=customerid from inserted
delete from customer where customer.customerid=@customerid

This deletes the records from the customer table. Is there a way wherein i can re use the deleted customerid field for creation of one more record? What i mean is if i delete a customer whose customerid is 1, can i use customer id=1 for some other customer just for proper utilization?