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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =6a(6) =11a(7) =28a(8) =51a(9) =242a(10) =532a(11) =1545a(12) =6188a(13) =16592a(14) =86940a(15) =302909a(16) =967523a(17) =3808673a(18) =23029861a(19) =71772352a(20) =484629531a(21) =1840886853a(22) =9376324526a(23) =37878035106a(24) =204542429832