Number of permutations with certain forbidden subsequences.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =14a(5) =42a(6) =132a(7) =428a(8) =1417a(9) =4757a(10) =16119a(11) =54963a(12) =188219a(13) =646460a(14) =2224944a(15) =7668915a(16) =26461005a(17) =91371594a(18) =315689675a(19) =1091166442a(20) =3772747245a(21) =13047503222a(22) =45131078409a(23) =156129312025a(24) =540181837728