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A308352
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Number of k-ary quasitrivial semigroups that have no neutral element on an n-element set.
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2
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0, 2, 8, 58, 492, 5074, 60888, 835482, 12895796, 221169970, 4172486496, 85872215290, 1914575169756, 45970251182418, 1182618181384424, 32451961380002458, 946163712877067460, 29208900504551394610, 951798961321369842864, 32647628386008050898810
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OFFSET
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1,2
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COMMENTS
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Number of k-ary associative and quasitrivial operations that have no neutral element on an n-element set.
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LINKS
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FORMULA
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a(n) ~ n! * (4-r) / ((r-1) * (r-3)^(n+1)), where r = -LambertW(-1, -2*exp(-3)). - Vaclav Kotesovec, Jun 05 2019
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MATHEMATICA
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nmax = 20; Rest[CoefficientList[Series[(1 - x)/(3 - 2*E^x + x), {x, 0, nmax}], x] * Range[0, nmax]!] (* Vaclav Kotesovec, Jun 05 2019 *)
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PROG
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(PARI) seq(n)={Vec(-1+serlaplace((1-x)/(x+3-2*exp(x))) + O(x*x^n), -n)} \\ Andrew Howroyd, Aug 19 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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