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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =4a(5) =2a(6) =13a(7) =10a(8) =1a(9) =63a(10) =48a(11) =9a(12) =356a(13) =293a(14) =68a(15) =3a(16) =2403a(17) =2036a(18) =557a(19) =44a(20) =18655a(21) =16213a(22) =4902a(23) =539a(24) =11a(25) =163988a(26) =145068a(27) =47203a(28) =6356a(29) =265