a(n) = sum( (-1)^(r+1)*(n-r)*r, r = 1..floor(n/2) ).

Terms

a(0) =1a(1) =2a(2) =-1a(3) =-2a(4) =6a(5) =8a(6) =-6a(7) =-8a(8) =15a(9) =18a(10) =-15a(11) =-18a(12) =28a(13) =32a(14) =-28a(15) =-32a(16) =45a(17) =50a(18) =-45a(19) =-50a(20) =66a(21) =72a(22) =-66a(23) =-72a(24) =91a(25) =98a(26) =-91a(27) =-98a(28) =120a(29) =128