Number of even-length integer partitions of 2n with integer mean.

Terms

a(0) =0a(1) =1a(2) =3a(3) =4a(4) =10a(5) =6a(6) =33a(7) =8a(8) =65a(9) =68a(10) =117a(11) =12a(12) =583a(13) =14a(14) =319a(15) =1078a(16) =1416a(17) =18a(18) =3341a(19) =20a(20) =8035a(21) =5799a(22) =1657a(23) =24a(24) =36708a(25) =16954a(26) =3496a(27) =24553a(28) =68528a(29) =30