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 A204044 Lozenge Gaussian integer factorial, product of all nonzero Gaussian integers a + bi for which |a| + |b| <= n. 2
 -1, 64, -3240000, 530841600000000, -791432829997056000000000000, 24298387172648346846064803840000000000000000, -30208456145049398593072092383690495361024000000000000000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Called "lozenge" because the Gaussian integers considered here form up a lozenge or diamond in the complex plane. All terms are purely real integers. LINKS FORMULA log |a(n)| ~ 2n^2 log n. - Charles R Greathouse IV, May 01 2012 EXAMPLE 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). MATHEMATICA Table[Times@@Select[ReplaceAll[Flatten[Table[a + b I, {a, -n, n}, {b, -n, n}]], 0 -> 1], Abs[Re[#]] + Abs[Im[#]] <= n&], {n, 10}] PROG (PARI) 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 CROSSREFS Cf. A204041, square factorial; A204043, circle factorial. Sequence in context: A329236 A013847 A017298 * A017418 A017550 A087928 Adjacent sequences:  A204041 A204042 A204043 * A204045 A204046 A204047 KEYWORD sign AUTHOR Alonso del Arte, Jan 09 2012 STATUS approved

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Last modified January 23 19:17 EST 2022. Contains 350515 sequences. (Running on oeis4.)