A063073 Square of determinant of character table of the dihedral group with 2n elements.

4, 256, 36, 4096, 500, 82944, 9604, 2097152, 236196, 64000000, 7086244, 2293235712, 250994068, 94450499584, 10251562500, 4398046511104, 474351505988, 228509902503936, 24524265031204, 13107200000000000

Offset: 1

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Aug 03 2001

Keywords

• nonn

Comments

For any finite group G with order n we have that if A is the character table then |det(A)|^2 = product i (n/c(i)) where the product is over the conjugacy classes of G: c(i), so by this formula the square of the determinant is an integer (in the case of dihedral groups the characters are real).

Links

• Harry J. Smith, Table of n, a(n) for n=1..200

Programs

PARI

{ for (n=1, 200, if (n%2, a=4 * n^((n+1)/2), a=64 * n^((n+2)/2)); write("b063073.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 16 2009

Formula

a(n) = 4 * n^((n+1)/2) if n odd, a(n)= 64 * n^((n+2)/2) if n even. - Paul Boddington, Oct 22 2003

Extensions

Missing term included and more terms added by Harry J. Smith, Aug 16 2009