Number of even-length integer partitions of n with integer alternating product.

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =3a(5) =2a(6) =6a(7) =4a(8) =11a(9) =8a(10) =18a(11) =13a(12) =33a(13) =22a(14) =49a(15) =38a(16) =79a(17) =58a(18) =122a(19) =90a(20) =186a(21) =139a(22) =268a(23) =206a(24) =402a(25) =304a(26) =569a(27) =448a(28) =817a(29) =636