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A052169
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Equivalent of the Kurepa hypothesis for left factorial.
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2
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1, 2, 5, 19, 91, 531, 3641, 28673, 254871, 2523223, 27526069, 328018989, 4239014627, 59043418019, 881715042417, 14052333488521, 238063061452591, 4271909380510383, 80941440893880941, 1614781745832924773
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OFFSET
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2,2
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COMMENTS
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a(n)=A002467(n)/(n-1) (A002467(n)=number of non-derangements of {1,2,...,n}). [From Emeric Deutsch, Jun 15 2009]
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LINKS
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Table of n, a(n) for n=2..21.
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
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FORMULA
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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 [From 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)) [From Gary Detlefs, Jul 11 2010]
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MAPLE
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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); [From Emeric Deutsch, Jun 15 2009]
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MATHEMATICA
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Numerator[k=1; NestList[1+1/(k++ #1)&, 1, 12]] - Wouter Meeussen, Mar 24 2007
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PROG
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(Sage) from sage.combinat.sloane_functions import ExtremesOfPermanentsSequence2 sage: e = ExtremesOfPermanentsSequence2() sage: it = e.gen(1, 2, 1) sage: [it.next() for i in range(20)] #(5 rows)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 15 2009]
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CROSSREFS
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Pairwise sums of A002467.
Sequence in context: A052324 A020115 A103816 * A020019 A020109 A020015
Adjacent sequences: A052166 A052167 A052168 * A052170 A052171 A052172
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KEYWORD
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nonn,easy
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AUTHOR
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Aleksandar Petojevic (apetoje(AT)ptt.yu), Jan 26 2000
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EXTENSIONS
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More terms from James A. Sellers, Jan 31 2000
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STATUS
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approved
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