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A283828
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Number of bounded regions in the Linial arrangement L_{n-1}.
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2
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0, 0, 1, 4, 26, 212, 2108, 24720, 334072, 5112544, 87396728, 1650607040, 34132685120, 767025716736, 18612106195456, 485013257865472, 13509071081429888, 400505695457942528, 12592502771190979712, 418524228123134068224, 14661145374751901317888
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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a(n) = (1/2^n) * Sum_{k=0..n} (k-1)^(n-1) * binomial(n,k) for n>=2.
In the following generating functions we take a(1)=1 rather than a(1)=0.
E.g.f.: 1 + (1/2)*x/LambertW(-(1/2)*x*exp(x/2)).
E.g.f.: 1-1/B(x), where B(x) is the e.g.f. of A007889. See Corollary 4.2 of Stanley's paper. (End)
a(n) ~ sqrt(1 + LambertW(exp(-1))) * n^(n-1) / (exp(n) * 2^n * LambertW(exp(-1))^(n-1)). - Vaclav Kotesovec, Nov 13 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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