Number of 1 up, 2 down, 3 up, 4 down, ... permutations of [n].

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =11a(6) =26a(7) =50a(8) =315a(9) =1168a(10) =3309a(11) =7910a(12) =78134a(13) =431354a(14) =1748956a(15) =5797168a(16) =16619603a(17) =239887424a(18) =1875375485a(19) =10496708022a(20) =47013492080a(21) =178807998112a(22) =599025922320