A204041 Square Gaussian integer factorial, product of all Gaussian integers except 0 having a real or imaginary part less than or equal to n.

-4, 2560000, -19188605030400000000, 26257841860510325145600000000000000000000, -50074374492086859469933185828103742596055040000000000000000000000000000

Offset: 1

Author

Alonso del Arte, Jan 09 2012

Keywords

• sign

Comments

This is called "square" because the Gaussian integers involved here form a square on the complex plane.

All terms are purely real integers, but a(6) has more than a hundred digits.

Examples

			a(1) = 1 * (1 + i) * i * (-1 + i) * -1 * (-1 - i) * -i * (1 - i) = -4.
		

Crossrefs

Cf. A204044, lozenge factorial; A204043, circle factorial.

Programs

Mathematica

Table[Times@@ReplaceAll[Flatten[Table[a + b I, {a, -n, n}, {b, -n, n}]], 0 -> 1], {n, 10}]