cp's OEIS Frontend

A234459 Real part of the product of all the integer complex numbers in the square [1,1] to [n,n].

%I A234459 #18 Aug 02 2018 15:19:36
%S A234459 1,-20,7800,530400000,2787453552000000,-7066368691421644800000000,
%T A234459 3108366378804858902744832000000000000,
%U A234459 1291087724942273632600239979303403520000000000000000
%N A234459 Real part of the product of all the integer complex numbers in the square [1,1] to [n,n].
%H A234459 Andrew Howroyd, <a href="/A234459/b234459.txt">Table of n, a(n) for n = 1..27</a>
%e A234459 For n = 2, we have (1 + i)(1 + 2i)(2 + i)(2 + 2i) which gives -20 + 0i, so a(2) = -20.
%t A234459 Table[Re[Times@@Flatten[Table[a + b I, {a, n}, {b, n}]]], {n, 20}] (* _Alonso del Arte_, Feb 04 2014 *)
%o A234459 (JavaScript)
%o A234459 function cNumber(x, y) {
%o A234459 return [x, y];
%o A234459 }
%o A234459 function cMult(a, b) {
%o A234459 return [a[0] * b[0] - a[1] * b[1], a[0] * b[1] + a[1] * b[0]];
%o A234459 }
%o A234459 for (i = 1; i < 10; i++) {
%o A234459 c = cNumber(1, 0);
%o A234459 for (j = 1; j <= i; j++)
%o A234459 for (k = 1; k <= i; k++)
%o A234459 c = cMult(c, cNumber(j, k));
%o A234459 document.write(c + "<br>");
%o A234459 }
%o A234459 (PARI) a(n) = real(prod(i=1, n, prod(j=1, n, i+I*j))); \\ _Michel Marcus_, Dec 27 2013
%Y A234459 Cf. A000142, A234460.
%K A234459 sign
%O A234459 1,2
%A A234459 _Jon Perry_, Dec 26 2013