Sequence arising in search for Legendre sequences.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =3a(6) =15a(7) =11a(8) =28a(9) =107a(10) =135a(11) =378a(12) =1201a(13) =1895a(14) =4696a(15) =20284a(16) =46250a(17) =77403a(18) =351918