Number of set partitions of [n] with nondecreasing block sizes.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =7a(5) =12a(6) =43a(7) =89a(8) =363a(9) =1096a(10) =4349a(11) =14575a(12) =77166a(13) =265648a(14) =1369284a(15) =6700177a(16) =33526541a(17) =162825946a(18) =1034556673a(19) =5157939218a(20) =33054650345a(21) =206612195885