A204043 Circle Gaussian integer factorial, product of all Gaussian integers except 0 having an absolute value less than or equal to n.

-1, 64, -207360000, 15161366937600000000, -16026514807440384000000000000000000000000, 9186394651457723405912022826165758590976000000000000000000000000

Offset: 1

Author

Alonso del Arte, Jan 09 2012

Keywords

• sign

Comments

Called "circle" because drawing a circle on the complex plane centered at 0 with radius n encloses the integers (with the exception of 0) that will be considered in computing a(n).

All terms of this sequence are purely real numbers.

Examples

			a(1) = 1 * i * -1 * -i = -1. (Note that numbers like -1 + i are ignored here).
a(5) = 5 * (4 + 3i) * (3 + 4i) * 5i * (-3 + 4i) * (-4 + 3i) * ... (Note that the absolute value of numbers like 4 + 3i is precisely 5).
		

Crossrefs

Cf. A204041, square factorial; A204044, lozenge factorial.

Programs

Mathematica

Table[Times@@Select[ReplaceAll[Flatten[Table[a + b I, {a, -n, n}, {b, -n, n}]], 0 -> 1], Abs[#] <= n &], {n, 10}]