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

Terms

a(0) =1a(1) =2a(2) =6a(3) =24a(4) =120a(5) =720a(6) =713a(7) =664a(8) =216a(9) =-4320a(10) =-54720a(11) =-664560a(12) =-664547a(13) =-664378a(14) =-661830a(15) =-620880a(16) =78000a(17) =12701520a(18) =12701501a(19) =12701140a(20) =12693540a(21) =12525960a(22) =8663640a(23) =-84207600a(24) =-84207575a(25) =-84206950a(26) =-84190050a(27) =-83716200a(28) =-69957000a(29) =343310400