Sequences A124174 and A006454 interlaced.

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =10a(5) =15a(6) =45a(7) =120a(8) =351a(9) =528a(10) =1540a(11) =4095a(12) =11935a(13) =17955a(14) =52326a(15) =139128a(16) =405450a(17) =609960a(18) =1777555a(19) =4726275a(20) =13773376a(21) =20720703a(22) =60384555a(23) =160554240a(24) =467889345a(25) =703893960a(26) =2051297326a(27) =5454117903a(28) =15894464365a(29) =23911673955