Obverse convolution (n)**(n*(-1)^n); see Comments.

Terms

a(0) =0a(1) =-1a(2) =0a(3) =-27a(4) =-256a(5) =1875a(6) =0a(7) =252105a(8) =4718592a(9) =-55801305a(10) =0a(11) =-18415376595a(12) =-515978035200a(14) =0a(18) =0a(22) =0