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A106540
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a(n) = a(n-1) - 2*a(n-2) - 3*a(n-3) - ... - (n-1)*a(1), with a(1) = a(2) = 1, a(3) = -1.
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3
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1, 1, -1, -6, -11, -5, 28, 87, 111, -46, -519, -1105, -812, 2051, 8003, 12130, 477, -43213, -107764, -106273, 133575, 716562, 1269265, 492135, -3436796, -10232533, -12529349, 6701026, 62284757, 128290443, 86849596, -256333913, -946668833
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = a(n-1) - Sum_{k=2..n-1} k*a(n-k), with a(1) = a(2) = 1, a(3) = -1.
G.f.: x*(1 - x)^2/(1 - 3*x + 5*x^2 - 2*x^3). - corrected by R. J. Mathar, Aug 22 2008
a(n) = 3*a(n-1) - 5*a(n-2) + 2*a(n-3). - G. C. Greubel, Sep 03 2021
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MATHEMATICA
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LinearRecurrence[{3, -5, 2}, {1, 1, -1}, 40] (* G. C. Greubel, Sep 03 2021 *)
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PROG
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(Magma) I:=[1, 1, -1]; [n le 3 select I[n] else 3*Self(n-1) - 5*Self(n-2) + 2*Self(n-3): n in [1..41]]; // G. C. Greubel, Sep 03 2021
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1-x)^2/(1-3*x+5*x^2-2*x^3) ).list()
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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