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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

Table of n, a(n) for n=1..7.

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: A017190 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 November 19 16:06 EST 2019. Contains 329320 sequences. (Running on oeis4.)