A236401 Kurepa determinant K_n.

15, -47, 197, -1029, 6439, -46927, 390249, -3645737, 37792331, -430400211, 5341017373, -71724018781, 1036207207363983, -16024176975479, 264083895859409, -4620276321889617, 85520275455047059, -1669635965205539227, 34287733935303686661

Offset

7,1

Comments

This is the value of a certain determinant of order n-4 (see Metrovic 2013 for definition).

Links

Table of n, a(n) for n=7..25.

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

Sequence in context: A214675 A166118 A063396 * A000813 A156205 A065906

Adjacent sequences: A236398 A236399 A236400 * A236402 A236403 A236404

Keyword

sign

Author

N. J. A. Sloane, Jan 29 2014

Status

approved