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A021129
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Expansion of 1/((1-x)(1-2x)(1-5x)(1-8x)).
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1
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1, 16, 175, 1650, 14481, 122316, 1010995, 8250550, 66817861, 538611216, 4329233415, 34735589850, 278393339641, 2229689837716, 17850234337435, 142865452943550, 1143241514899821, 9147521576217816, 73188119895363055
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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)=16, a(2)=175, a(3)=1650; for n>3, a(n) = 16*a(n-1) -81*a(n-2) +146*a(n-3) -80*a(n-4). - Vincenzo Librandi, Jul 07 2013
a(0)=1, a(1)=16; for n>1, a(n) = 13*a(n-1) -40*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 07 2013
a(n) = (2*8^(n+3) - 7*5^(n+3) + 14*2^(n+3) - 9)/252. [Yahia Kahloune, Jul 07 2013]
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MATHEMATICA
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CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 5 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 07 2013 *)
LinearRecurrence[{16, -81, 146, -80}, {1, 16, 175, 1650}, 30] (* Harvey P. Dale, Nov 12 2021 *)
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PROG
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(Magma) I:=[1, 16, 175, 1650]; [n le 4 select I[n] else 16*Self(n-1)-81*Self(n-2)+146*Self(n-3)-80*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-5*x)*(1-8*x)))); // Vincenzo Librandi, Jul 07 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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