a(n) = [x^(n*(n+1)/2)] Product_{k=1..n} Sum_{m>=0} x^(k*m^2).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =6a(6) =20a(7) =51a(8) =141a(9) =381a(10) =1001a(11) =2796a(12) =7861a(13) =22306a(14) =64129a(15) =185692a(16) =540468a(17) =1585246a(18) =4674464a(19) =13846636a(20) =41216933a(21) =123176849a(22) =369410571a(23) =1111661833a(24) =3355466306a(25) =10156304314a(26) =30821794651a(27) =93761053797a(28) =285859742756a(29) =873355481467