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

Terms

a(0) =1a(1) =2a(2) =6a(3) =24a(4) =120a(5) =720a(6) =5040a(7) =5032a(8) =4968a(9) =4320a(10) =-2880a(11) =-90000a(12) =-1230480a(13) =-17292240a(14) =-17292225a(15) =-17292000a(16) =-17288160a(17) =-17218800a(18) =-15896880a(19) =10614960a(20) =568758960a(21) =568758938a(22) =568758454a(23) =568746816a(24) =568455360a(25) =560865360a(26) =355631760a(27) =-5398802640a(28) =-5398802611