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, 29917468619617547059200, 957358995827761505894400, 137859695399197656848793600

Offset

1,3

Links

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

Formula

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

Prog

(SageMath)
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

Crossrefs

Cf. A001088, A060238.

Sequence in context: A182967 A013049 A193155 * A127943 A012498 A180745

Adjacent sequences: A060236 A060237 A060238 * A060240 A060241 A060242

Keyword

sign

Author

John McKay (mckay(AT)cs.concordia.ca), Mar 21 2001

Status

approved