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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 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

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