cp's OEIS Frontend

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

%I A234460 #22 Aug 04 2018 14:29:28
%S A234460 1,0,7800,0,2787453552000000,0,3108366378804858902744832000000000000,
%T A234460 0,
%U A234460 165290679439545659068950724771043004678057040281600000000000000000000,0
%N A234460 Imaginary part of the product of all the integer complex numbers in the square [1,1] to [n,n].
%H A234460 Andrew Howroyd, <a href="/A234460/b234460.txt">Table of n, a(n) for n = 1..28</a>
%F A234460 For n even, a(n) = 0, and for n odd, a(n) = A234459(n). - _Michel Marcus_, Dec 31 2013
%e A234460 For n = 2, we have (1 + i)(1 + 2i)(2 + i)(2 + 2i) which gives -20 + 0i, so a(2) = 0.
%t A234460 Table[Im[Times@@Flatten[Table[a + b I, {a, n}, {b, n}]]], {n, 20}]
%o A234460 (JavaScript)
%o A234460 function cNumber(x, y) {
%o A234460 return [x, y];
%o A234460 }
%o A234460 function cMult(a, b) {
%o A234460 return [a[0] * b[0] - a[1] * b[1], a[0] * b[1] + a[1] * b[0]];
%o A234460 }
%o A234460 for (i = 1; i < 10; i++) {
%o A234460 c = cNumber(1, 0);
%o A234460 for (j = 1; j <= i; j++)
%o A234460 for (k = 1; k <= i; k++)
%o A234460 c = cMult(c, cNumber(j, k));
%o A234460 document.write(c + "<br>");
%o A234460 }
%o A234460 (PARI) a(n) = imag(prod(i=1, n, prod(j=1, n, i+I*j))); \\ _Michel Marcus_, Dec 31 2013
%Y A234460 Cf. A000142, A234459.
%K A234460 nonn
%O A234460 1,3
%A A234460 _Jon Perry_, Dec 26 2013