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 A330352 Expansion of e.g.f. -Sum_{k>=1} log(1 - log(1 + x)^k) / k. 6
 1, 1, 0, 10, -68, 818, -9782, 130730, -1835752, 27408672, -438578616, 7697802264, -150743052528, 3293454634416, -78787556904864, 2014008113598432, -54001416897306240, 1504891127666322048, -43527807706621236480, 1311515508480252542208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..400 FORMULA 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. MATHEMATICA 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}] CROSSREFS 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 KEYWORD sign AUTHOR Ilya Gutkovskiy, Dec 11 2019 STATUS approved

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Last modified March 25 07:00 EDT 2023. Contains 361511 sequences. (Running on oeis4.)