cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A204043 #8 Mar 30 2012 17:27:26
%S A204043 -1,64,-207360000,15161366937600000000,
%T A204043 -16026514807440384000000000000000000000000,
%U A204043 9186394651457723405912022826165758590976000000000000000000000000
%N A204043 Circle Gaussian integer factorial, product of all Gaussian integers except 0 having an absolute value less than or equal to n.
%C A204043 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).
%C A204043 All terms of this sequence are purely real numbers.
%e A204043 a(1) = 1 * i * -1 * -i = -1. (Note that numbers like -1 + i are ignored here).
%e A204043 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).
%t A204043 Table[Times@@Select[ReplaceAll[Flatten[Table[a + b I, {a, -n, n}, {b, -n, n}]], 0 -> 1], Abs[#] <= n &], {n, 10}]
%Y A204043 Cf. A204041, square factorial; A204044, lozenge factorial.
%K A204043 sign
%O A204043 1,2
%A A204043 _Alonso del Arte_, Jan 09 2012