Sequence arising in search for Legendre sequences.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =6a(5) =14a(6) =66a(7) =95a(8) =280a(9) =1464a(10) =2694a(11) =10452a(12) =41410a(13) =95640a(14) =323396a(15) =1770963a(16) =5405026a(17) =13269146a(18) =73663402a(19) =164107650a(20) =582538732a(21) =3811895344a(22) =7457847082a(23) =30712068524a(24) =151938788640a(25) =353218528324