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A021144
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Expansion of 1/((1-x)(1-2x)(1-5x)(1-10x)).
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1
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1, 18, 227, 2520, 26481, 271278, 2745247, 27615060, 276964061, 2773708938, 27757433067, 277676053200, 2777269152841, 27775234648998, 277765062125687, 2777714199500940, 27777459886360821, 277776188320627458
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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)=18, a(2)=227, a(3)=2520; for n>2, a(n) = 18*a(n-1) -97*a(n-2) +180*a(n-3) -100*a(n-4). - Vincenzo Librandi, Jul 07 2013
a(0)=1, a(1)=18; for n>1, a(n) = 15*a(n-1)-50*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 07 2013
a(n) = (10^(n+3) - 6*5^(n+3) + 15*2^(n+3) - 10)/360. [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 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 07 2013 *)
LinearRecurrence[{18, -97, 180, -100}, {1, 18, 227, 2520}, 30] (* Harvey P. Dale, Aug 24 2015 *)
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PROG
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(Magma) I:=[1, 18, 227, 2520]; [n le 4 select I[n] else 18*Self(n-1)-97*Self(n-2)+180*Self(n-3)-100*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)*(1-10*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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