Number of permutations with certain forbidden subsequences.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =14a(5) =42a(6) =132a(7) =429a(8) =1429a(9) =4847a(10) =16660a(11) =57820a(12) =202086a(13) =709928a(14) =2503266a(15) =8850681a(16) =31355020a(17) =111242127a(18) =395091069a(19) =1404332528a(20) =4994581900a(21) =17771328588a(22) =63253477326a(23) =225194224134a(24) =801884971816