It's the sequence of odd numbers with alternating signs.

The sequence of positive odd integers 1,3,5,7,9,... has general
term  2n-1  (one less than the general term for the even integers, 2n)

To cause the signs to alternate, beginning with the first term being
positive, we must multiply by the factor (-1)n+1.  So the 
general term is

tn = (-1)n+1(2n-1)

Edwin