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

Terms

a(0) =1a(1) =2a(2) =6a(3) =24a(4) =19a(5) =-6a(6) =-186a(7) =-1656a(8) =-1647a(9) =-1566a(10) =-666a(11) =10224a(12) =10211a(13) =10042a(14) =7494a(15) =-33456a(16) =-33439a(17) =-33150a(18) =-27642a(19) =82824a(20) =82803a(21) =82362a(22) =72198a(23) =-172200a(24) =-172175a(25) =-171550a(26) =-154650a(27) =319200a(28) =319171a(29) =318330