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A068024
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Z(S_m; sigma[1](n), sigma[2](n),..., sigma[m](n)) where Z(S_m; x_1,x_2,...,x_m) is the cycle index of the symmetric group S_m and sigma[k](n) is the sum of k-th powers of divisors of n; m=7.
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2
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1, 255, 3280, 43435, 97656, 998184, 960800, 6347715, 8069620, 27615060, 21435888, 184770040, 67977560, 263540112, 343123440, 866251507, 435984840, 2595218340, 943531280, 4944199260, 3308659904, 5722701624, 3559590240
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OFFSET
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1,2
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LINKS
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FORMULA
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1/7!*(sigma[1](n)^7 + 21*sigma[1](n)^5*sigma[2](n) + 70*sigma[1](n)^4*sigma[3](n) + 105*sigma[1](n)^3*sigma[2](n)^2 + 210*sigma[1](n)^3*sigma[4](n) + 420*sigma[1](n)^2*sigma[2](n)*sigma[3](n) + 105*sigma[1](n)*sigma[2](n)^3 + 504*sigma[1](n)^2*sigma[5](n) + 630*sigma[1](n)*sigma[2](n)*sigma[4](n) + 280*sigma[1](n)*sigma[3](n)^2 + 210*sigma[2](n)^2*sigma[3](n) + 840*sigma[1](n)*sigma[6](n) + 504*sigma[2](n)*sigma[5](n) + 420*sigma[3](n)*sigma[4](n) + 720*sigma[7](n)).
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MATHEMATICA
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CIP7 = CycleIndexPolynomial[SymmetricGroup[7], Array[x, 7]]; a[n_] := CIP7 /. x[k_] -> DivisorSigma[k, n]; Array[a, 23] (* Jean-François Alcover, Nov 04 2016 *)
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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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