A228548 Determinant of the n X n matrix with (i,j)-entry equal to A008683(i+j-1) for all i,j = 1..n.

1, -2, 3, 3, -7, -5, 12, -19, -52, -52, -20, 73, -919, 6209, 2206, -1869, -8835, -4021, 23202, -122489, -174347, 1106682, 1114088, 388318, -7528057, 55753005, 81020413, -530178192, -6348221604, 101952770365, -371734984964, -16091176203501, 90823940064758, 163339092651834, -3480231557696967

Offset: 1

Author

Zhi-Wei Sun, Aug 25 2013

Keywords

• sign

Comments

Conjecture: a(n) is always nonzero. Moreover, |a(n)|^(1/n) tends to infinity.

We have verified that a(n) is nonzero for all n = 1..500.

Examples

			a(1) = 1 since Moebius(1+1-1) = 1.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A008683, A228549, A069191, A228552.

Programs

Mathematica

a[n_]:=a[n]=Det[Table[MoebiusMu[i+j-1],{i,1,n},{j,1,n}]]
Table[a[n],{n,1,10}]

PARI

a(n) = matdet(matrix(n, n, i, j, moebius(i+j-1))); \\ Michel Marcus, Apr 14 2023