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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =4a(5) =11a(6) =36a(7) =82a(8) =239a(9) =821a(10) =3742a(11) =10328a(12) =42934a(13) =156070a(14) =729249a(15) =4025361a(16) =15032099a(17) =68746675a(18) =334541624a(19) =1645575386a(20) =9104991312a(21) =65010298257a(22) =282768687257