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A234460 Imaginary part of the product of all the integer complex numbers in the square [1,1] to [n,n]. 2

%I

%S 1,0,7800,0,2787453552000000,0,3108366378804858902744832000000000000,

%T 0,

%U 165290679439545659068950724771043004678057040281600000000000000000000,0

%N Imaginary part of the product of all the integer complex numbers in the square [1,1] to [n,n].

%H Andrew Howroyd, <a href="/A234460/b234460.txt">Table of n, a(n) for n = 1..28</a>

%F For n even, a(n) = 0, and for n odd, a(n) = A234459(n). - _Michel Marcus_, Dec 31 2013

%e For n = 2, we have (1 + i)(1 + 2i)(2 + i)(2 + 2i) which gives -20 + 0i, so a(2) = 0.

%t Table[Im[Times@@Flatten[Table[a + b I, {a, n}, {b, n}]]], {n, 20}]

%o (JavaScript)

%o function cNumber(x, y) {

%o return [x, y];

%o }

%o function cMult(a, b) {

%o return [a[0] * b[0] - a[1] * b[1], a[0] * b[1] + a[1] * b[0]];

%o }

%o for (i = 1; i < 10; i++) {

%o c = cNumber(1, 0);

%o for (j = 1; j <= i; j++)

%o for (k = 1; k <= i; k++)

%o c = cMult(c, cNumber(j, k));

%o document.write(c + "<br>");

%o }

%o (PARI) a(n) = imag(prod(i=1, n, prod(j=1, n, i+I*j))); \\ _Michel Marcus_, Dec 31 2013

%Y Cf. A000142, A234459.

%K nonn

%O 1,3

%A _Jon Perry_, Dec 26 2013

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Last modified July 29 09:31 EDT 2021. Contains 346344 sequences. (Running on oeis4.)