a(n) = Sum_{j=0..n} Sum_{k=0..j} Stirling2(j - k, k).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =9a(6) =18a(7) =40a(8) =98a(9) =262a(10) =757a(11) =2344a(12) =7723a(13) =26918a(14) =98790a(15) =380361a(16) =1531699a(17) =6434386a(18) =28130891a(19) =127729731a(20) =601196429a(21) =2928369918a(22) =14738842362a(23) =76547694742a(24) =409718539682