Triangle of transformations with k monotonic runs.

Terms

a(0) =1a(1) =3a(2) =1a(3) =10a(4) =16a(5) =1a(6) =35a(7) =155a(8) =65a(9) =1a(10) =126a(11) =1246a(12) =1506a(13) =246a(14) =1a(15) =462a(16) =9142a(17) =24017a(18) =12117a(19) =917a(20) =1a(21) =1716a(22) =63792a(23) =315918a(24) =349840a(25) =88852a(26) =3424a(27) =1a(28) =6435a(29) =432399