a(n)=det(M_n) where M_n is the n X n matrix m(i,j)=1 if sigma(i+j) is odd, 0 otherwise.

Terms

a(0) =1a(1) =1a(2) =-1a(3) =-1a(4) =0a(5) =1a(6) =-5a(7) =-4a(8) =-3a(9) =13a(10) =16a(11) =-5a(12) =1a(13) =-1a(14) =-8a(15) =-48a(16) =32a(17) =39a(18) =99a(19) =78a(20) =-307a(21) =333a(22) =603a(23) =-35a(24) =-1068a(25) =936a(26) =-444a(27) =-1619a(28) =-595a(29) =5104