A177066 Determinant of the symmetric n X n matrix M defined by M(i,j) = gcd(2i-1,2j-1) for 1 <= i,j <= n.

1, 2, 8, 48, 288, 2880, 34560, 276480, 4423680, 79626240, 955514880, 21021327360, 420426547200, 7567677849600, 211894979788800, 6356849393664000, 127136987873280000, 3051287708958720000, 109846357522513920000

Offset: 1

Author

John W. Layman, Dec 09 2010

Keywords

• nonn

Comments

It appears, but has not been proved, that the ratios a(n+1)/a(n) give phi(2n+1) (A037225).

See A001088, A059381, and A059382 for determinants of matrices M defined by M(i,j) = gcd(i,j), gcd(i^2,j^2), and gcd(i^3,j^3), respectively.

Crossrefs

Cf. A001088, A037225, A059381, A059382.

Programs

Maple

A177066 := proc(n) M := Matrix(n) ; for i from 1 to n do for j from 1 to n do M[i,j] := igcd(2*i-1,2*j-1) ; end do: end do: LinearAlgebra[Determinant](M) ; end proc: # R. J. Mathar, Dec 10 2010