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A338814
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Expansion of e.g.f. log(Product_{k>0} (1 + x^k)^(1/k)).
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4
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1, 0, 4, -6, 48, 0, 1440, -10080, 120960, 0, 7257600, -79833600, 958003200, 0, 348713164800, -3923023104000, 41845579776000, 0, 12804747411456000, -243290200817664000, 9731608032706560000, 0, 2248001455555215360000, -103408066955539906560000
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OFFSET
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1,3
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LINKS
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FORMULA
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MATHEMATICA
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a[n_] := (n - 1)! * DivisorSum[n, (-1)^(# + 1) &]; Array[a, 25] (* Amiram Eldar, Apr 28 2021 *)
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PROG
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(PARI) N=40; x='x+O('x^N); Vec(serlaplace(log(prod(k=1, N, (1+x^k)^(1/k)))))
(PARI) {a(n) = if(n<1, 0, (n-1)!*sumdiv(n, d, (-1)^(d+1)))}
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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