A173936 The determinant of an n X n matrix derived from the matrix X(s,k) = s^2 - 2*s + k.

0, -3, 42, -532, 7280, -110816, 1878912, -35290368, 729151488, -16458706944, 403306168320, -10667511152640, 303026291343360, -9203027198607360, 297626965251194880, -10212876839131545600, 370647479637717811200, -14185745639287868620800, 571060601049504861388800

Offset

1,2

Comments

Start from an auxiliary infinite matrix X with entries X(s,k) = s^2 - 2*s + k, with indices s, k >= 1.

Build a matrix T by preserving the subdiagonal triangular part of X and filling the superdiagonal triangular part of T by reading X with a 90-degree hook at the diagonal: T(m,k) = X(m,k) if m >= k and T(m,k) = X(k,2k-m) if m < k. Imagine reading X along columns along decreasing row number and continuing along increasing column number after reaching the diagonal. Then a(n) = determinant(T).

Links

Table of n, a(n) for n=1..19.

Formula

a(n) = (-2)^(n-2)*(n-1)!*((Sum_{k=1..n-1} 1/k) - 2*n*(n-1)).

Maple

with(linalg) : X := proc(s, k) s^2-2*s+k ; end proc:
A173936 := proc(n) T := matrix(n, n) ; for m from 1 to n do for k from 1 to n do if m >= k then T[m, k] := X(m, k) ; else T[m, k] := X(k, 2*k-m) ; end if; end do ; end do ; det(T) ; end proc:
seq(A173936(n), n=1..20) ; # R. J. Mathar, Mar 05 2010

Crossrefs

Sequence in context: A084522 A160874 A003770 * A219619 A097068 A269046

Adjacent sequences: A173933 A173934 A173935 * A173937 A173938 A173939

Keyword

sign

Author

Anonymous, Mar 03 2010

Extensions

Extended and description simplified by R. J. Mathar, Mar 05 2010

Status

approved