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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =7a(5) =17a(6) =52a(7) =144a(8) =480a(9) =1732a(10) =5902a(11) =21078a(12) =78434a(13) =289107a(14) =1079949a(15) =4094643a(16) =15574377a(17) =59667023a(18) =230318968a(19) =892694240a(20) =3477119540a(21) =13606993083a(22) =53438614380a(23) =210622413188a(24) =832922044686