Number of 1 up, 1 down, 2 up, 2 down, ... permutations of [n].

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =9a(6) =40a(7) =111a(8) =643a(9) =2261a(10) =6176a(11) =53560a(12) =265001a(13) =976535a(14) =10699235a(15) =65839306a(16) =297528021a(17) =1096638993a(18) =16254932942a(19) =131192702293a(20) =760059358527