a(n) = 1*2*3*4*5*6*7*8 - 9*10*11*12*13*14*15*16 + 17*18*19*20*21*22*23*24 - ... + (up to n).

Terms

a(0) =1a(1) =2a(2) =6a(3) =24a(4) =120a(5) =720a(6) =5040a(7) =40320a(8) =40311a(9) =40230a(10) =39330a(11) =28440a(12) =-114120a(13) =-2121840a(14) =-32392080a(15) =-518878080a(16) =-518878063a(17) =-518877774a(18) =-518872266a(19) =-518761800a(20) =-516436200a(21) =-465156720a(22) =716713200a(23) =29135312640a(24) =29135312615a(25) =29135311990a(26) =29135295090a(27) =29134821240