a(n) = A000124(n)*a(n-3) for n > 2, otherwise n!.

Terms

a(0) =1a(1) =1a(2) =2a(3) =7a(4) =11a(5) =32a(6) =154a(7) =319a(8) =1184a(9) =7084a(10) =17864a(11) =79328a(12) =559636a(13) =1643488a(14) =8408768a(15) =67715956a(16) =225157856a(17) =1294950272a(18) =11647144432a(19) =43005150496a(20) =273234507392