Number of permutations in S_{n+3} containing an increasing subsequence of length n.

Terms

a(0) =6a(1) =24a(2) =119a(3) =588a(4) =2279a(5) =6996a(6) =18043a(7) =40884a(8) =83923a(9) =159404a(10) =284431a(11) =482108a(12) =782799a(13) =1225508a(14) =1859379a(15) =2745316a(16) =3957723a(17) =5586364a(18) =7738343a(19) =10540204a(20) =14140151a(21) =18710388a(22) =24449579a(23) =31585428a(24) =40377379a(25) =51119436a(26) =64143103a(27) =79820444a(28) =98567263a(29) =120846404