Number of 4 up, 4 down permutations of [n].

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =5a(7) =15a(8) =35a(9) =70a(10) =574a(11) =2674a(12) =9274a(13) =26599a(14) =305747a(15) =1944033a(16) =8995805a(17) =33757360a(18) =498851248a(19) =4017418768a(20) =23236611280a(21) =107709888805