a(n) = p*(p-1)/2, where p is A000043(n).

Terms

a(0) =1a(1) =3a(2) =10a(3) =21a(4) =78a(5) =136a(6) =171a(7) =465a(8) =1830a(9) =3916a(10) =5671a(11) =8001a(12) =135460a(13) =183921a(14) =817281a(15) =2425503a(16) =2600340a(17) =5172936a(18) =9041878a(19) =9779253a(20) =46933516a(21) =49406770a(22) =62860078a(23) =198732016a(24) =235455850a(25) =269317236a(26) =989969256a(27) =3718884403a(28) =6105401253a(29) =8718403176