a(n) = Sum_{k=0..floor(n/3)} |Stirling1(n - 2*k,n - 3*k)|.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =4a(6) =7a(7) =13a(8) =27a(9) =57a(10) =120a(11) =262a(12) =593a(13) =1361a(14) =3171a(15) =7559a(16) =18356a(17) =45186a(18) =112927a(19) =286689a(20) =737641a(21) =1921639a(22) =5070154a(23) =13540352a(24) =36566737a(25) =99830013a(26) =275459693a(27) =767798853a(28) =2160953618a(29) =6139721116