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A094734
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Number of connected 2-element multiantichains on a labeled n-set.
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1
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0, 1, 1, 4, 19, 76, 271, 904, 2899, 9076, 27991, 85504, 259579, 784876, 2366911, 7125304, 21425059, 64373476, 193317031, 580344304, 1741819339, 5227030876, 15684238351, 47059006504, 141189602419, 423593973076, 1270832250871, 3812597415904, 11437993574299
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OFFSET
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0,4
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LINKS
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FORMULA
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E.g.f.: (1/2!)*(exp(3*x) - 3*exp(2*x) + 5*exp(x) - 3).
a(n) = (5 - 3*2^n + 3^n)/2 for n > 0.
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n > 3.
G.f.: -x*(9*x^2-5*x+1)/((x-1)*(2*x-1)*(3*x-1)). (End)
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MATHEMATICA
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Join[{0}, LinearRecurrence[{6, -11, 6}, {1, 1, 4}, 30]] (* Harvey P. Dale, Nov 28 2014 *)
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PROG
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(PARI) x='x+O('x^50); concat([0], Vec(serlaplace((1/2!)*(exp(3*x) - 3*exp(2*x) + 5*exp(x) - 3)))) \\ G. C. Greubel, Oct 07 2017
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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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EXTENSIONS
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STATUS
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approved
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