Number of strongly monotone partitions of [n].

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =22a(6) =58a(7) =164a(8) =496a(9) =1601a(10) =5502a(11) =20075a(12) =77531a(13) =315947a(14) =1354279a(15) =6087421a(16) =28611385a(17) =140239297a(18) =715116827a(19) =3785445032a(20) =20760746393a(21) =117759236340a(22) =689745339984