Bitriangular permutations.

Terms

a(0) =1a(1) =13a(2) =73a(3) =301a(4) =1081a(5) =3613a(6) =11593a(7) =36301a(8) =111961a(9) =342013a(10) =1038313a(11) =3139501a(12) =9467641a(13) =28501213a(14) =85700233a(15) =257493901a(16) =773268121a(17) =2321377213a(18) =6967277353a(19) =20908123501a(20) =62736953401a(21) =188236026013a(22) =564758409673