a(n)=(-1)^(n+1)*det(M(n)) where M(n) is the n X n matrix M(i,j)=min(abs(i-j),i).

Terms

a(0) =0a(1) =1a(2) =3a(3) =8a(4) =18a(5) =40a(6) =88a(7) =192a(8) =400a(9) =832a(10) =1728a(11) =3584a(12) =7424a(13) =15360a(14) =31744a(15) =65536a(16) =133120a(17) =270336a(18) =548864a(19) =1114112a(20) =2260992a(21) =4587520a(22) =9306112a(23) =18874368a(24) =38273024a(25) =77594624a(26) =157286400a(27) =318767104a(28) =645922816a(29) =1308622848