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A200864
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Expansion of 1/((1+x)*(1-3*x)*(1-5*x)).
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2
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1, 7, 42, 230, 1211, 6237, 31732, 160300, 806421, 4046867, 20278622, 101525970, 508028431, 2541337897, 12710276712, 63562145240, 317843011241, 1589311911327, 7946850122002, 39735122306110, 198678226618851, 993398978359157, 4967018427590492, 24835162745336580
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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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G.f.: 1/((1+x)*(1-3*x)*(1-5*x)).
a(n) = (50*5^n-27*3^n+(-1)^n)/24.
a(n) = 2*a(n-1)+3*a(n-2)+5^n for n>1, a(0)=1, a(1)=7.
a(n) = 7*a(n-1)-7*a(n-2)-15*a(n-3) for n>2, a(0)=1, a(1)=7, a(2)=42.
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MATHEMATICA
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CoefficientList[Series[1/((1+x)(1-3x)(1-5x)), {x, 0, 24}], x]
LinearRecurrence[{7, -7, -15}, {1, 7, 42}, 30] (* Harvey P. Dale, May 26 2015 *)
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PROG
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(PARI) Vec(1/((1+x)*(1-3*x)*(1-5*x))+O(x^24))
(Magma) m:=24; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1+x)*(1-3*x)*(1-5*x))));
(Maxima) makelist(coeff(taylor(1/((1+x)*(1-3*x)*(1-5*x)), x, 0, n), x, n), n, 0, 23);
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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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