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).
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
KEYWORD
sign
AUTHOR
Anonymous, Mar 03 2010
EXTENSIONS
Extended and description simplified by R. J. Mathar, Mar 05 2010
STATUS
approved