Triangle read by rows: T(n, k) = [x^k]( (n+2)!*(3*EulerE(n, x+1) - EulerE(n, x))/4 ).

Terms

a(0) =1a(1) =3a(2) =3a(3) =0a(4) =24a(5) =12a(6) =-30a(7) =0a(8) =180a(9) =60a(10) =0a(11) =-720a(12) =0a(13) =1440a(14) =360a(15) =2520a(16) =0a(17) =-12600a(18) =0a(19) =12600a(20) =2520a(21) =0a(22) =120960a(23) =0a(24) =-201600a(25) =0a(26) =120960a(27) =20160a(28) =-771120a(29) =0