A060239 a(n) = determinant(P*Q)/n! where P, Q are n X n matrices with P[i,j]=lcm(i,j), Q[i,j]=gcd(i,j).

1, -1, 4, -8, 128, 512, -18432, 73728, -884736, -14155776, 1415577600, 11324620800, -1630745395200, -58706834227200, -3757237390540800, 30057899124326400, -7694822175827558400, -92337866109930700800

Offset: 1

Author

MCKAY john (mckay(AT)cs.concordia.ca), Mar 21 2001

Keywords

• sign

Links

• Enrique Pérez Herrero, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A001088, A060238.

Programs

Sage

def A060239(n):
    P = Matrix(lambda i,j: lcm(i+1,j+1), nrows=n)
    Q = Matrix(lambda i,j: gcd(i+1,j+1), nrows=n)
    return (P*Q).det()/factorial(n) # D. S. McNeil, Jan 16 2011

Formula

a(n) = A001088(n)*A060238(n)/n!.