Irregular triangle read by rows: T(n,k) = number of "pat" permutations of [1..n] with k descents.

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =2a(5) =0a(6) =1a(7) =4a(8) =0a(9) =0a(10) =12a(11) =2a(12) =0a(13) =0a(14) =12a(15) =30a(16) =0a(17) =0a(18) =4a(19) =100a(20) =28a(21) =0a(22) =0a(23) =0a(24) =140a(25) =280a(26) =9a(27) =0a(28) =0a(29) =0