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A021404
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Expansion of 1/((1-x)(1-3x)(1-4x)(1-12x)).
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1
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1, 20, 285, 3640, 44681, 540540, 6505045, 78138080, 937976961, 11257033060, 135089723405, 1621098253320, 19453266126841, 233439544261580, 2801275941271365, 33615316957309360, 403383826200494321
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OFFSET
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0,2
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LINKS
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FORMULA
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a(0)=1, a(1)=20, a(2)=285, a(3)=3640, a(n) = 20*a(n-1)-115*a(n-2)+240*a(n-3)- 144*a(n-4). [Harvey P. Dale, May 06 2012]
a(0)=1, a(1)=20; for n>1, a(n) = 16*a(n-1) -48*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013
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MATHEMATICA
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CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 12 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{20, -115, 240, -144}, {1, 20, 285, 3640}, 30] (* Harvey P. Dale, May 06 2012 *)
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PROG
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(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-12*x)))); /* or */ I:=[1, 20, 285, 3640]; [n le 4 select I[n] else 20*Self(n-1)-115*Self(n-2)+240*Self(n-3)-144*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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