Riordan array (1/(1+2xc(-2x)),xc(-2x)/(1+2xc(-2x))), c(x) the g.f. of A000108.

Terms

a(0) =1a(1) =-2a(2) =1a(3) =8a(4) =-6a(5) =1a(6) =-40a(7) =36a(8) =-10a(9) =1a(10) =224a(11) =-224a(12) =80a(13) =-14a(14) =1a(15) =-1344a(16) =1440a(17) =-600a(18) =140a(19) =-18a(20) =1a(21) =8448a(22) =-9504a(23) =4400a(24) =-1232a(25) =216a(26) =-22a(27) =1a(28) =-54912a(29) =64064