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A008675
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Expansion of 1/( Product_{j=0..5} (1-x^(2*j+1)) ).
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2
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1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 21, 25, 29, 34, 40, 46, 53, 62, 70, 80, 91, 103, 116, 131, 147, 164, 184, 204, 227, 252, 278, 307, 339, 372, 408, 448, 489, 534, 583, 634, 689, 749, 811, 878, 950, 1025, 1106, 1192, 1282, 1378, 1481, 1588, 1702, 1823, 1949, 2083
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OFFSET
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0,4
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COMMENTS
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Number of partitions of n into parts 1, 3, 5, 7, 9, and 11. - Joerg Arndt, Jul 09 2013
Number of partitions (d1,d2,...,d6) of n such that 0 <= d1/1 <= d2/2 <= ... <= d6/6. - Seiichi Manyama, Jun 04 2017
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, -1, 1, -1, 1, -2, 2, -2, 2, -3, 2, -2, 3, -3, 3, -2, 3, -3, 3, -2, 2, -3, 2, -2, 2, -2, 1, -1, 1, -1, 1, 0, 1, -1).
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MAPLE
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seq(coeff(series(1/mul(1-x^(2*j+1), j=0..5), x, n+1), x, n), n = 0..65); # G. C. Greubel, Sep 08 2019
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MATHEMATICA
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CoefficientList[Series[1/((1-x)(1-x^3)(1-x^5)(1-x^7)(1-x^9)(1-x^11)), {x, 0, 65}], x] (* Vincenzo Librandi, Jun 23 2013 *)
LinearRecurrence[{1, 0, 1, -1, 1, -1, 1, -2, 2, -2, 2, -3, 2, -2, 3, -3, 3, -2, 3, -3, 3, -2, 2, -3, 2, -2, 2, -2, 1, -1, 1, -1, 1, 0, 1, -1}, {1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 21, 25, 29, 34, 40, 46, 53, 62, 70, 80, 91, 103, 116, 131, 147, 164, 184, 204, 227, 252, 278, 307}, 60] (* Harvey P. Dale, Oct 29 2022 *)
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PROG
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(PARI) a(n)=(46200*((n\3+1)*[2, -1, -1][n%3+1]+[10, -4, -7][n%3+1]) +3*n^5+ 270*n^4+9005*n^3+136350*n^2+908260*n+3603600)\3742200 \\ Tani Akinari, Jul 09 2013
(PARI) Vec(1/((1-x)*(1-x^3)*(1-x^5)*(1-x^7)*(1-x^9)*(1-x^11))+O(x^66)) \\ Joerg Arndt, Jul 09 2013
(Magma) R<x>:=PowerSeriesRing(Integers(), 65); Coefficients(R!( 1/&*[1-x^(2*j+1): j in [0..5]] )); // G. C. Greubel, Sep 08 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/prod(1-x^(2*j+1) for j in (0..5)) ).list()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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