Swinging factorial, a(n) = 2^(n-(n mod 2))*Product_{k=1..n} k^((-1)^(k+1)).

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =6a(5) =30a(6) =20a(7) =140a(8) =70a(9) =630a(10) =252a(11) =2772a(12) =924a(13) =12012a(14) =3432a(15) =51480a(16) =12870a(17) =218790a(18) =48620a(19) =923780a(20) =184756a(21) =3879876a(22) =705432a(23) =16224936a(24) =2704156a(25) =67603900a(26) =10400600a(27) =280816200a(28) =40116600a(29) =1163381400