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A236401 Kurepa determinant K_n. 1
15, -47, 197, -1029, 6439, -46927, 390249, -3645737, 37792331, -430400211, 5341017373, -71724018781, 1036207207363983, -16024176975479, 264083895859409, -4620276321889617, 85520275455047059, -1669635965205539227, 34287733935303686661 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified August 1 05:51 EDT 2021. Contains 346384 sequences. (Running on oeis4.)