A054516 - OEIS

%I #27 Sep 16 2022 15:27:10

%S 0,2,2,6,-4,50,-258,1862,-14824,133506,-1334950,14684582,-176214828,

%T 2290792946,-32071101034,481066515750,-7697064251728,130850092279682,

%U -2355301661033934,44750731559645126,-895014631192902100,18795307255050944562,-413496759611120779858

%N Equivalent of the Kurepa hypothesis for left factorial.

%H G. C. Greubel, <a href="/A054516/b054516.txt">Table of n, a(n) for n = 3..450</a>

%H Romeo Mestrovic, <a href="http://arxiv.org/abs/1312.7037">Variations of Kurepa's left factorial hypothesis</a>, arXiv:1312.7037 [math.NT], 2013.

%H Romeo Mestrovic, <a href="https://doi.org/10.2298/FIL1510207M">The Kurepa-Vandermonde matrices arising from Kurepa's left factorial hypothesis</a>, Filomat 29:10 (2015), 2207-2215; DOI 10.2298/FIL1510207M.

%H A. Petojevic, M. Zizovic, <a href="http://elib.mi.sanu.ac.rs/files/journals/flmt/14/flmn14p31-40.pdf">Trees and the Kurepa hypothesis for left factorial</a>, Filomat (Nis), (1999), 31-40.

%F a(3) = 0, a(n) = -(n-3)*a(n-1) + (n-3)*(n-2).

%F Conjecture: (-n+4)*a(n) + (-n^2+8*n-14)*a(n-1) + (n-2)*(n-4)*a(n-2) = 0. - _R. J. Mathar_, Jan 31 2014

%t (* Assuming offset 0 *)

%t Table[(-1)^n*n*((-1)^n - Subfactorial[n - 1]), {n,0,20}] (* _Peter Luschny_, Dec 30 2016 *)

%t RecurrenceTable[{a[n]+(n-3)*a[n-1]==(n-2)*(n-3), a[3]==0}, a, {n,3,30}] (* _G. C. Greubel_, Mar 30 2019 *)

%o (PARI) m=30; v=concat([0], vector(m-1)); for(n=2, m, v[n]=-(n-1)*v[n-1] + n*(n-1)); v \\ _G. C. Greubel_, Mar 30 2019

%o (Magma) [n eq 3 select 0 else -(n-3)*Self(n-3) + (n-2)*(n-3): n in [3..30]]; // _G. C. Greubel_, Mar 30 2019

%o (Sage)

%o @CachedFunction

%o def Self(n):

%o    if n == 3 : return 0

%o    return -(n-3)*Self(n-1) + (n-2)*(n-3)

%o [Self(n) for n in (3..30)] # _G. C. Greubel_, Mar 30 2019

%K sign,easy

%O 3,2

%A _Aleksandar Petojevic_, Apr 09 2000

%E More terms from _James A. Sellers_, Apr 09 2000