Triangle of rank k of permutations of {1,2,...,n}.

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =0a(5) =1a(6) =2a(7) =1a(8) =1a(9) =2a(10) =6a(11) =4a(12) =3a(13) =2a(14) =9a(15) =24a(16) =18a(17) =14a(18) =11a(19) =9a(20) =44a(21) =120a(22) =96a(23) =78a(24) =64a(25) =53a(26) =44a(27) =265a(28) =720a(29) =600