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A328193
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Expansion of e.g.f. Sum_{k>=1} log(1/(1 + (-x)^k/k)).
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1
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1, 0, 4, 3, 48, 10, 1440, 1890, 85120, 49896, 7257600, 6883800, 958003200, 792277200, 178919989248, 194107914000, 41845579776000, 29714949264000, 12804747411456000, 12900082757417856, 4918792391884800000, 4594737608304480000, 2248001455555215360000
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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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a(n) = n! * Sum_{d|n} (-1)^(n - d) / (d * (n/d)^d).
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MAPLE
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a:= n-> n!*add((-1)^(n-d)/(d*(n/d)^d), d=numtheory[divisors](n)):
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MATHEMATICA
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nmax = 23; CoefficientList[Series[Sum[Log[1/(1 + (-x)^k/k)], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! Sum[(-1)^(n - d)/(d (n/d)^d), {d, Divisors[n]}], {n, 1, 23}]
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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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