A204041
Square Gaussian integer factorial, product of all Gaussian integers except 0 having a real or imaginary part less than or equal to n.
Original entry on oeis.org
-4, 2560000, -19188605030400000000, 26257841860510325145600000000000000000000, -50074374492086859469933185828103742596055040000000000000000000000000000
Offset: 1
a(1) = 1 * (1 + i) * i * (-1 + i) * -1 * (-1 - i) * -i * (1 - i) = -4.
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Table[Times@@ReplaceAll[Flatten[Table[a + b I, {a, -n, n}, {b, -n, n}]], 0 -> 1], {n, 10}]
A204044
Lozenge Gaussian integer factorial, product of all nonzero Gaussian integers a + bi for which |a| + |b| <= n.
Original entry on oeis.org
-1, 64, -3240000, 530841600000000, -791432829997056000000000000, 24298387172648346846064803840000000000000000, -30208456145049398593072092383690495361024000000000000000000000000
Offset: 1
a(2) = -2 * (-1 - i) * -1 * (-1 + i) * -2i * -i * i * 2i * (1 - i) * 1 * (1 + i) * 2 = 64. (Note that numbers like -2 + i are skipped over in the computation of a(2) because abs(-2) + abs(1) > 2).
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Table[Times@@Select[ReplaceAll[Flatten[Table[a + b I, {a, -n, n}, {b, -n, n}]], 0 -> 1], Abs[Re[#]] + Abs[Im[#]] <= n&], {n, 10}]
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a(n)=(-1)^n*prod(i=1,n,prod(j=1,n-i,i^2+j^2))^2*n!^4 \\ Charles R Greathouse IV, May 01 2012
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