a(n) = floor(C(n + 1/2)), where C = A000108.

Terms

a(0) =0a(1) =1a(2) =3a(3) =8a(4) =24a(5) =74a(6) =237a(7) =781a(8) =2630a(9) =9020a(10) =31375a(11) =110442a(12) =392685a(13) =1408249a(14) =5087870a(15) =18501347a(16) =67662072a(17) =248703832a(18) =918291072a(19) =3404396173a(20) =12667520643a(21) =47292077070a(22) =177093735411a(23) =665005047259