Riordan array (1/(1-3x*c(x)),xc(x)), c(x) the g.f. of A000108.

Terms

a(0) =1a(1) =3a(2) =1a(3) =12a(4) =4a(5) =1a(6) =51a(7) =17a(8) =5a(9) =1a(10) =222a(11) =74a(12) =23a(13) =6a(14) =1a(15) =978a(16) =326a(17) =104a(18) =30a(19) =7a(20) =1a(21) =4338a(22) =1446a(23) =468a(24) =142a(25) =38a(26) =8a(27) =1a(28) =19323a(29) =6441