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

1,1

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.

Links

Table of n, a(n) for n=1..5.

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A046362 A144122 A058424 * A065248 A116141 A225876

Adjacent sequences: A204038 A204039 A204040 * A204042 A204043 A204044

Keyword

sign

Author

Alonso del Arte, Jan 09 2012

Status

approved