Number of 3 up, 3 down permutations of [n].

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =4a(6) =10a(7) =20a(8) =125a(9) =461a(10) =1301a(11) =11210a(12) =55220a(13) =202840a(14) =2223859a(15) =13690951a(16) =61889101a(17) =823947856a(18) =6087160726a(19) =32676403052a(20) =511799407517