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A308345
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Expansion of e.g.f. Sum_{k>=1} log(1/(1 - x^k/k)).
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5
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1, 2, 4, 15, 48, 310, 1440, 11970, 85120, 821016, 7257600, 91707000, 958003200, 13440913200, 178919989248, 2809456650000, 41845579776000, 763629026160000, 12804747411456000, 257140635922025856, 4918792391884800000, 106876408948152480000
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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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a(n) = n! * Sum_{d|n} 1/(d*(n/d)^d).
a(n) = A007841(n) - (1/n) * Sum_{k=1..n-1} k*binomial(n,k)*A007841(n-k)*a(k).
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MATHEMATICA
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nmax = 22; CoefficientList[Series[Sum[Log[1/(1 - x^k/k)], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! Sum[1/(d (n/d)^d), {d, Divisors[n]}], {n, 1, 22}]
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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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