Alternating row sums of the Eulerian zig-zag number triangle A205497.

Terms

a(0) =1a(1) =-1a(2) =1a(3) =0a(4) =-1a(5) =0a(6) =5a(7) =0a(8) =-45a(9) =0a(10) =665a(11) =0a(12) =-14457a(13) =0a(14) =433741a(15) =0a(16) =-17160421a(17) =0a(18) =865407905a(19) =0a(20) =-54179057649a(21) =0a(23) =0a(25) =0a(27) =0a(29) =0a(31) =0a(33) =0