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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).
3

%I #9 Mar 14 2020 11:27:23

%S 1,-1,4,-8,128,512,-18432,73728,-884736,-14155776,1415577600,

%T 11324620800,-1630745395200,-58706834227200,-3757237390540800,

%U 30057899124326400,-7694822175827558400,-92337866109930700800

%N 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).

%H Enrique PĂ©rez Herrero, <a href="/A060239/b060239.txt">Table of n, a(n) for n = 1..100</a>

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

%o (Sage)

%o def A060239(n):

%o P = Matrix(lambda i,j: lcm(i+1,j+1), nrows=n)

%o Q = Matrix(lambda i,j: gcd(i+1,j+1), nrows=n)

%o return (P*Q).det()/factorial(n) # _D. S. McNeil_, Jan 16 2011

%Y Cf. A001088, A060238.

%K sign

%O 1,3

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