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A014670
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G.f.: (1+x)*(1+x^3)*(1+x^5)*(1+x^7)*(1+x^9)/((1-x^2)*(1-x^4)*(1-x^6)*(1-x^8)*(1-x^10)).
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7
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1, 1, 1, 2, 3, 4, 5, 7, 10, 13, 16, 20, 26, 32, 38, 47, 58, 69, 81, 96, 114, 133, 153, 177, 206, 236, 267, 304, 346, 390, 437, 490, 550, 613, 679, 753, 835, 921, 1011, 1111, 1221, 1335, 1455, 1586, 1728, 1877, 2032, 2200, 2382, 2571, 2768, 2980, 3207, 3443, 3689, 3952
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OFFSET
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0,4
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COMMENTS
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Poincaré series [or Poincare series] (or Molien series) for symmetric invariants in F_2(b_1, b_2, ... b_n) ⊗ E(e_1, e_2, ... e_n) with b_i 2-dimensional, e_i one-dimensional and the permutation action of S_n, in the case n=5.
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REFERENCES
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A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 108.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (3, -5, 8, -11, 14, -18, 21, -23, 24, -24, 23, -21, 18, -14, 11, -8, 5, -3, 1).
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FORMULA
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G.f.: -(x^2-x+1) *(x^6-x^5+x^4-x^3+x^2-x+1) *(x^6-x^3+1) / ( (x^4+x^3+x^2+x+1) *(1+x+x^2) *(x^4+1) *(x^2+1)^2 *(x-1)^5 ). - R. J. Mathar, Dec 18 2014
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1+x^3)*(1+x^5)*(1+x^7)*(1+x^9)/((1-x^2)*(1-x^4)*(1-x^6)*(1-x^8)*(1-x^10)), {x, 0, 50}], x] (* Jinyuan Wang, Mar 10 2020 *)
LinearRecurrence[{3, -5, 8, -11, 14, -18, 21, -23, 24, -24, 23, -21, 18, -14, 11, -8, 5, -3, 1}, {1, 1, 1, 2, 3, 4, 5, 7, 10, 13, 16, 20, 26, 32, 38, 47, 58, 69, 81}, 60] (* Harvey P. Dale, Mar 28 2023 *)
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PROG
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(PARI) Vec((1+x)*(1+x^3)*(1+x^5)*(1+x^7)*(1+x^9)/((1-x^2)*(1-x^4)*(1-x^6)*(1-x^8)*(1-x^10))+ O(x^100)) \\ Michel Marcus, Mar 18 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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