Triangle read by rows: T(n,k) = number of permutations of [n] allowing i->i+j (mod n), j=0..k-1.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =2a(5) =6a(6) =1a(7) =2a(8) =9a(9) =24a(10) =1a(11) =2a(12) =13a(13) =44a(14) =120a(15) =1a(16) =2a(17) =20a(18) =80a(19) =265a(20) =720a(21) =1a(22) =2a(23) =31a(24) =144a(25) =579a(26) =1854a(27) =5040a(28) =1a(29) =2