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A094034
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Number of connected 3-element antichains on a labeled n-set.
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3
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0, 0, 0, 1, 38, 645, 7510, 71981, 617358, 4947685, 37972070, 283229661, 2072354878, 14964711125, 107078983830, 761312910541, 5388481567598, 38017703680965, 267622831854790, 1880882526962621, 13203901505935518, 92616363612417205
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OFFSET
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0,5
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LINKS
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FORMULA
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E.g.f.: (exp(7*x) - 6*exp(5*x) + 3*exp(4*x) + 14*exp(3*x) - 21*exp(2*x) + 11*exp(x) -2)/3!.
G.f.: -x^3*(5*x+1)*(56*x^2-11*x-1) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(7*x-1)). - Colin Barker, Nov 27 2012
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MATHEMATICA
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With[{nmax = 50}, CoefficientList[Series[(Exp[7*x] - 6*Exp[5*x] + 3*Exp[4*x] + 14*Exp[3*x] - 21*Exp[2*x] + 11*Exp[x] - 2)/3!, {x, 0, nmax}], x] Range[0, nmax]!] (* G. C. Greubel, Oct 07 2017 *)
LinearRecurrence[{22, -190, 820, -1849, 2038, -840}, {0, 0, 0, 1, 38, 645, 7510}, 30] (* Harvey P. Dale, Sep 20 2022 *)
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PROG
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(PARI) x='x+O('x^50); concat([0, 0, 0], Vec(-x^3*(5*x+1)*(56*x^2-11*x-1)/( (x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(7*x-1)))) \\ 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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STATUS
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approved
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