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A321898
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Sum of coefficients of power sums symmetric functions in h(y) * Product_i y_i! where h is homogeneous symmetric functions and y is the integer partition with Heinz number n.
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2
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1, 1, 2, 1, 6, 2, 24, 1, 4, 6, 120, 2, 720, 24, 12, 1, 5040, 4, 40320, 6, 48, 120, 362880, 2, 36, 720, 8, 24, 3628800, 12, 39916800, 1, 240, 5040, 144, 4, 479001600, 40320, 1440, 6, 6227020800, 48, 87178291200, 120, 24, 362880, 1307674368000, 2, 576, 36, 10080
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OFFSET
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1,3
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COMMENTS
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The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
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LINKS
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FORMULA
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EXAMPLE
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The sum of coefficients of 12h(32) = 2p(32) + 3p(221) + 2p(311) + 4p(2111) + p(11111) is a(15) = 12.
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MATHEMATICA
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f[p_, e_] := (PrimePi[p]!)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Sep 10 2023 *)
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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