Number of permutations of [n] avoiding {3412, 3421, 1324}.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =21a(5) =73a(6) =240a(7) =744a(8) =2192a(9) =6192a(10) =16896a(11) =44800a(12) =115968a(13) =294144a(14) =733184a(15) =1800192a(16) =4362240a(17) =10448896a(18) =24772608a(19) =58195968a(20) =135593984a(21) =313589760a(22) =720371712a(23) =1644691456a(24) =3733979136a(25) =8433696768a(26) =18958254080a(27) =42429579264a(28) =94573166592a(29) =210000412672