Number of permutations of length n sortable by 3 passes through a pop-stack.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =24a(5) =88a(6) =303a(7) =1033a(8) =3544a(9) =12220a(10) =42164a(11) =145364a(12) =500954a(13) =1726408a(14) =5950050a(15) =20507364a(16) =70680192a(17) =243602952a(18) =839588620a(19) =2893682172a(20) =9973219220a(21) =34373198420a(22) =118468937648a(23) =408309065104