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A052169 Equivalent of the Kurepa hypothesis for left factorial. 5
1, 2, 5, 19, 91, 531, 3641, 28673, 254871, 2523223, 27526069, 328018989, 4239014627, 59043418019, 881715042417, 14052333488521, 238063061452591, 4271909380510383, 80941440893880941, 1614781745832924773, 33833522293642233339, 742799603083145395579 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

a(n) = A002467(n)/(n-1) (A002467(n) = number of non-derangements of {1,2,...,n}). - Emeric Deutsch, Jun 15 2009

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..450

Juan S. Auli, Sergi Elizalde, Consecutive patterns in inversion sequences II: avoiding patterns of relations, arXiv:1906.07365 [math.CO], 2019. See Table 1, p. 6.

T. Kotek, J. A. Makowsky, Recurrence Relations for Graph Polynomials on Bi-iterative Families of Graphs, arXiv preprint arXiv:1309.4020 [math.CO], 2013.

Romeo Mestrovic, Variations of Kurepa's left factorial hypothesis, arXiv preprint arXiv:1312.7037 [math.NT], 2013.

Romeo Mestrovic, The Kurepa-Vandermonde matrices arising from Kurepa's left factorial hypothesis, Filomat 29:10 (2015), 2207-2215; DOI 10.2298/FIL1510207M.

Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7.

FORMULA

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

a(n) = 2*floor((n+1)!*(n+3)/e+1/2) - 3*(floor(((n+1)!+1)/e)+ floor(((n+2)!+1)/e)) +(n+1)!+(n+2)!, n>1, with offset 0..a(0)= 1. - Gary Detlefs, Apr 18 2010

a(n) = 1/(n+1)*((n+2)!-floor(((n+2)!+1)/e)), with offset 0 a(n) = 1/(n-1)*(n! - floor((n!+1)/e)). - Gary Detlefs, Jul 11 2010

From Benedict W. J. Irwin, Jun 02 2016: (Start)

Let y(-1)=1, y(0)=1,

Let y(n) = (Sum_{k=0,n-1} y(k)+y(k-1))/n,

a(n) = (n-2)!y(n-2).

(End)

MAPLE

a[2] := 1: a[3] := 2: for n from 4 to 21 do a[n] := (n-2)*a[n-1]+(n-3)*a[n-2] end do: seq(a[n], n = 2 .. 21); # Emeric Deutsch, Jun 15 2009

# second Maple program:

a:= proc(n) option remember; `if`(n<4, n-1,

      (n-2)*a(n-1)+(n-3)*a(n-2))

    end:

seq(a(n), n=2..25);  # Alois P. Heinz, Aug 30 2016

MATHEMATICA

Numerator[k=1; NestList[1+1/(k++ #1)&, 1, 12]] (* Wouter Meeussen, Mar 24 2007 *)

a[n_] := (n! - Subfactorial[n])/(n-1); Table[a[n], {n, 2, 23}] {* Jean-Fran├žois Alcover, Jul 21 2017, after Emeric Deutsch's comment *)

PROG

(Sage) from sage.combinat.sloane_functions import ExtremesOfPermanentsSequence2 ; e = ExtremesOfPermanentsSequence2() ; it = e.gen(1, 2, 1) ; [it.next() for i in range(20)] #(5 rows) # Zerinvary Lajos, May 15 2009

CROSSREFS

Pairwise sums of A002467.

Sequence in context: A052324 A020115 A103816 * A020019 A020109 A020015

Adjacent sequences:  A052166 A052167 A052168 * A052170 A052171 A052172

KEYWORD

nonn,easy

AUTHOR

Aleksandar Petojevic (apetoje(AT)ptt.yu), Jan 26 2000

EXTENSIONS

More terms from James A. Sellers, Jan 31 2000

STATUS

approved

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Last modified January 25 07:38 EST 2020. Contains 331241 sequences. (Running on oeis4.)