A diagonal of A008296.

Terms

a(0) =1a(1) =3a(2) =-1a(3) =0a(4) =4a(5) =-28a(6) =188a(7) =-1368a(8) =11016a(9) =-98208a(10) =964512a(11) =-10370880a(12) =121337280a(13) =-1535880960a(14) =20924455680a(15) =-305396421120