a(n) = n*a(n-1) + n^signum(n mod 4), a(0) = 1.

Terms

a(0) =1a(1) =2a(2) =6a(3) =21a(4) =85a(5) =430a(6) =2586a(7) =18109a(8) =144873a(9) =1303866a(10) =13038670a(11) =143425381a(12) =1721104573a(13) =22374359462a(14) =313241032482