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

1, 0, 7800, 0, 2787453552000000, 0, 3108366378804858902744832000000000000, 0, 165290679439545659068950724771043004678057040281600000000000000000000, 0

Offset: 1

Author

Jon Perry, Dec 26 2013

Keywords

• nonn

Examples

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..28

Crossrefs

Cf. A000142, A234459.

Programs

JavaScript

function cNumber(x, y) {
return [x, y];
}
function cMult(a, b) {
return [a[0] * b[0] - a[1] * b[1], a[0] * b[1] + a[1] * b[0]];
}
for (i = 1; i < 10; i++) {
c = cNumber(1, 0);
for (j = 1; j <= i; j++)
for (k = 1; k <= i; k++)
c = cMult(c, cNumber(j, k));
document.write(c + "
");
}

Mathematica

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

PARI

a(n) = imag(prod(i=1, n, prod(j=1, n, i+I*j))); \\ Michel Marcus, Dec 31 2013

Formula

For n even, a(n) = 0, and for n odd, a(n) = A234459(n). - Michel Marcus, Dec 31 2013