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A003048
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a(n+1)=n*a(n)-(-1)^n.
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1
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1, 2, 3, 10, 39, 196, 1175, 8226, 65807, 592264, 5922639, 65149030, 781788359, 10163248668, 142285481351, 2134282220266, 34148515524255, 580524763912336, 10449445750422047, 198539469258018894
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..20.
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FORMULA
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E.g.f.: (2-exp(-x))/(1-x) (if offset 0).
a(n+2)=n(a(n)+a(n+1)) for n>0. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Oct 05 2002
a(n) = 2*(n-1)! - floor(((n-1)!+1)/e), n>1 [From Gary Detlefs, Apr 11 2010]
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MAPLE
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a:= proc(p) option remember; p*a(p-1)-(-1)^p end proc: a(0):= 1: seq(a(p), p=0..19); - Robert Israel, Jan 05 2008
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MATHEMATICA
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a[0] = 1; a[p_] := p*a[p - 1] -(-1)^p; a /@ Range[0, 19] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 29 2007
FoldList[#1*#2 - (-1)^#2 &, 1, Range[19]] (* Robert G. Wilson v, Jul 07 2012 *)
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PROG
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(PARI) a(n)=if(n<2, n>0, (n-1)*a(n-1)+(-1)^n)
(PARI) a(n)=if(n<1, 0, (n-1)!*polcoeff((2-exp(-x+O(x^n)))/(1-x), n-1))
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CROSSREFS
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a(n)=(n-1)!+A002467(n), n>0.
Sequence in context: A141102 A144720 A164933 * A008980 A064183 A050381
Adjacent sequences: A003045 A003046 A003047 * A003049 A003050 A003051
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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