a(n) = n!*b(n) where b(n) = (b(n-2) + b(n-3))/(n*(n-1)), b(0) = b(1) = b(2) = 1.

Terms

a(0) =1a(1) =1a(2) =2a(3) =2a(4) =4a(5) =8a(6) =12a(7) =28a(8) =60a(9) =112a(10) =284a(11) =652a(12) =1404a(13) =3776a(14) =9228a(15) =22028a(16) =62092a(17) =160448a(18) =414540a(19) =1216012a(20) =3302604a(21) =9092272a(22) =27622844a(23) =78446956a(24) =227652828a(25) =713772368a(26) =2110379772a(27) =6405093068a(28) =20668461340a(29) =63385346912