Triangle read by rows: T(n,k) is the number of permutations of [n] having k fixed blocks.

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =1a(5) =2a(6) =4a(7) =0a(8) =9a(9) =12a(10) =3a(11) =44a(12) =57a(13) =18a(14) =1a(15) =265a(16) =321a(17) =123a(18) =11a(19) =1854a(20) =2176a(21) =888a(22) =120a(23) =2a(24) =14833a(25) =17008a(26) =7218a(27) =1208a(28) =53a(29) =133496