A122685 a(n) = n! except that a(2) = -2 and a(2n) = 0 for n > 2.

1, 1, -2, 6, 0, 120, 0, 5040, 0, 362880, 0, 39916800, 0, 6227020800, 0, 1307674368000, 0, 355687428096000, 0, 121645100408832000, 0, 51090942171709440000, 0, 25852016738884976640000, 0, 15511210043330985984000000, 0, 10888869450418352160768000000, 0, 8841761993739701954543616000000