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A204043 Circle Gaussian integer factorial, product of all Gaussian integers except 0 having an absolute value less than or equal to n. 2
-1, 64, -207360000, 15161366937600000000, -16026514807440384000000000000000000000000, 9186394651457723405912022826165758590976000000000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

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).

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A017418 A017550 A087928 * A295175 A279290 A034061

Adjacent sequences:  A204040 A204041 A204042 * A204044 A204045 A204046

KEYWORD

sign

AUTHOR

Alonso del Arte, Jan 09 2012

STATUS

approved

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Last modified January 23 16:29 EST 2022. Contains 350514 sequences. (Running on oeis4.)