OFFSET
7,1
COMMENTS
This is the value of a certain determinant of order n-4 (see Metrovic 2013 for definition).
LINKS
Romeo Mestrovic, Variations of Kurepa's left factorial hypothesis, arXiv preprint arXiv:1312.7037 [math.NT], 2013-2014.
Romeo Mestrovic, The Kurepa-Vandermonde matrices arising from Kurepa's left factorial hypothesis, Filomat 29:10 (2015), 2207-2215; DOI 10.2298/FIL1510207M.
FORMULA
Conjecture: a(n) ~ -(-1)^n * n! * exp(-1) / n^4. - Vaclav Kotesovec, Nov 30 2017
MAPLE
A236401 := proc(n)
local M, r, c ;
M := Matrix(n-4, n-4) ;
for r from 1 to n-4 do
for c from 1 to n-4 do
if r = 1 then
if c < n-4 then
M[r, c] := 1 ;
else
M[r, c] := 3 ;
end if;
elif r = n-4 then
if c = n-4 then
M[r, c] := -4 ;
elif c = n-5 then
M[r, c] := 1 ;
else
M[r, c] := 0 ;
end if;
elif c = n-4 then
M[r, c] := 2 ;
elif r > c+2 then
M[r, c] := 0 ;
elif r = c+2 then
M[r, c] := 1 ;
elif r = c+1 then
M[r, c] := r+1 ;
elif c = n-4 then
M[r, c] := 2 ;
else
M[r, c] := 1 ;
end if
end do:
end do:
LinearAlgebra[Determinant](M) ;
end proc:
seq(A236401(n), n=7..25) ;
MATHEMATICA
A236401[n_] := Det[Table[Which[
r == 1, If[c < n - 4, 1, 3],
r == n - 4, Which[
c == n - 4, -4,
c == n - 5, 1,
True, 0],
c == n - 4, 2,
r > c + 2, 0,
r == c + 2, 1,
r == c + 1, r + 1,
c == n - 4, 2,
True, 1],
{r, 1, n - 4}, {c, 1, n - 4}]];
Table[A236401[n], {n, 7, 25}] (* Jean-François Alcover, Nov 30 2017, from Maple *)
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Jan 29 2014
STATUS
approved