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A330498
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Expansion of e.g.f. Sum_{k>=1} log(1 + log(1/(1 - x))^k) / k.
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2
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0, 1, 1, 6, 24, 152, 1230, 12646, 141274, 1730984, 23920800, 379364664, 6766026168, 131337466608, 2713274041296, 59397879195456, 1386647548658496, 34745321580075648, 934708252265232768, 26835517455387452928, 815158892950448937984
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OFFSET
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0,4
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n = 0..400
Vaclav Kotesovec, Graph - the asymptotic ratio
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FORMULA
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a(n) ~ n! * c / (n * (1 - exp(-1))^n), where c = 0.6931..., conjecture: c = log(2).
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MATHEMATICA
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nmax = 20; CoefficientList[Series[Sum[Log[1+Log[1/(1-x)]^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
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CROSSREFS
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Cf. A003713, A330352, A330493, A330499.
Sequence in context: A026947 A250743 A265883 * A165491 A165638 A122829
Adjacent sequences: A330495 A330496 A330497 * A330499 A330500 A330501
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, Dec 16 2019
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STATUS
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approved
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