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

1,2

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.

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A008683, A228549, A069191, A228552.

Sequence in context: A141061 A256447 A076557 * A140407 A063670 A253357

Adjacent sequences: A228545 A228546 A228547 * A228549 A228550 A228551

Keyword

sign

Author

Zhi-Wei Sun, Aug 25 2013

Status

approved