A002415 and A052472 interlaced.

Terms

a(0) =1a(1) =0a(2) =2a(3) =1a(4) =0a(5) =6a(6) =10a(7) =20a(8) =35a(9) =50a(10) =84a(11) =105a(12) =168a(13) =196a(14) =300a(15) =336a(16) =495a(17) =540a(18) =770a(19) =825a(20) =1144a(21) =1210a(22) =1638a(23) =1716a(24) =2275a(25) =2366a(26) =3080a(27) =3185a(28) =4080a(29) =4200