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A330352
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Expansion of e.g.f. -Sum_{k>=1} log(1 - log(1 + x)^k) / k.
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6
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1, 1, 0, 10, -68, 818, -9782, 130730, -1835752, 27408672, -438578616, 7697802264, -150743052528, 3293454634416, -78787556904864, 2014008113598432, -54001416897306240, 1504891127666322048, -43527807706621236480, 1311515508480252542208
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OFFSET
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1,4
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n = 1..400
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FORMULA
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E.g.f.: Sum_{i>=1} Sum_{j>=1} log(1 + x)^(i*j) / (i*j).
E.g.f.: log(Product_{k>=1} 1 / (1 - log(1 + x)^k)^(1/k)).
a(n) = Sum_{k=1..n} Stirling1(n,k) * (k - 1)! * tau(k), where tau = A000005.
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MATHEMATICA
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nmax = 20; CoefficientList[Series[-Sum[Log[1 - Log[1 + x]^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[Sum[StirlingS1[n, k] (k - 1)! DivisorSigma[0, k], {k, 1, n}], {n, 1, 20}]
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CROSSREFS
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Cf. A000005, A002744, A008275, A028342, A089064, A318249, A330351, A330353, A330354, A330493.
Sequence in context: A027242 A081656 A219466 * A321060 A026958 A026988
Adjacent sequences: A330349 A330350 A330351 * A330353 A330354 A330355
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KEYWORD
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sign
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AUTHOR
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Ilya Gutkovskiy, Dec 11 2019
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STATUS
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approved
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