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A099242
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(6n+5)-th terms of expansion of 1/(1 - x - x^6).
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4
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1, 7, 34, 153, 686, 3088, 13917, 62721, 282646, 1273690, 5739647, 25864698, 116554700, 525233175, 2366870474, 10665883415, 48063918336, 216591552484, 976031547888, 4398313653120, 19820223058176, 89316331907533
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: 1/((1-x)^6-x).
a(n) = 7*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
a(n) = Sum_{k=0..n} binomial(6*n-5*(k-1), k).
a(n) = Sum_{k=0..n} binomial(n+5*(k+1), k+5*(k+1).
a(n) = Sum_{k=0..n} binomial(n+5*(k+1), n-k).
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MATHEMATICA
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CoefficientList[Series[1/((1 - x)^6 - x), {x, 0, 50}], x] (* G. C. Greubel, Nov 24 2017 *)
LinearRecurrence[{7, -15, 20, -15, 6, -1}, {1, 7, 34, 153, 686, 3088}, 30] (* Harvey P. Dale, May 06 2018 *)
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PROG
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(PARI) my(x='x+O('x^50)); Vec(1/((1-x)^6-x)) \\ G. C. Greubel, Nov 24 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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