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A025883
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Expansion of 1/((1-x^5)*(1-x^7)*(1-x^9)).
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5
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1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 4, 3, 4, 3, 4, 4, 4, 5, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 11, 10, 11, 11, 11, 12, 11
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OFFSET
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0,15
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COMMENTS
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a(n) is the number of partitions of n into parts 5, 7, and 9. - Joerg Arndt, Nov 19 2022
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,0,1,0,1,0,0,-1,0,-1,0,-1,0,0,0,0,1).
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MATHEMATICA
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CoefficientList[Series[1/((1-x^5)(1-x^7)(1-x^9)), {x, 0, 100}], x] (* or *)
LinearRecurrence[{0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 1, 1, 1, 1, 2, 1}, 100] (* Harvey P. Dale, Jun 24 2021 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Rationals(), 90); Coefficients(R!( 1/((1-x^5)*(1-x^7)*(1-x^9)) )); // G. C. Greubel, Nov 18 2022
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1-x^5)*(1-x^7)*(1-x^9)) ).list()
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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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