A061913 Numerators of the determinant of matrix (M(n) - H(n)), where H(n) is the n-th Hilbert matrix and M(n) is an n X n matrix with i,j-th entry i+j-1.

1, 0, -9, 32, -337, 319, -347, 1609, -21569, 21911, -82601, 12211, -247249, 50003, -624457, 16297, -42209, 91127, -91159, 488749, -1773467, 1782853, -9429289, 6156767, -548213, 376169, -25705577, 732761, -84793, 343823, -60683401, 36941321, -89392129, 53762297, -1478431

Offset: 0

Author

Asher Auel, May 20 2001

Keywords

• sign
• frac

Comments

The n-th Hilbert matrix is an n X n matrix with i,j-th entry 1/(i+j-1). Thus (M(n) - H(n)) has i,j-th entry (i+j-1) - 1/(i+j-1).

Crossrefs

Cf. A005249, A380297 (denominators).

Programs

Mathematica

a[n_]:=Numerator[Det[Table[(i+j-1) - 1/(i+j-1),{i,n},{j,n}]]]; Join[{1},Array[a,34]] (* Stefano Spezia, Jan 19 2025 *)

PARI

a(n) = numerator(matdet(matrix(n, n, i, j, (i+j-1) - 1/(i+j-1)))); \\ Michel Marcus, Jan 19 2025

Extensions

a(0) = 1 prepended by Stefano Spezia, Jan 19 2025