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%I #16 Oct 13 2017 15:49:24
%S 0,0,0,0,20,1655,65305,1794730,40179930,793030245,14423331635,
%T 248261291960,4113063835540,66327037011235,1049050826515965,
%U 16360528085273190,252545239130514350,3869090307434050625,58948119057416280295,894447719738683138420
%N Number of connected 4-element antichains on a labeled n-set.
%H G. C. Greubel, <a href="/A094035/b094035.txt">Table of n, a(n) for n = 0..845</a>
%F E.g.f.: (exp(15*x) - 12*exp(11*x) + 24*exp(9*x) - 14*exp(7*x) + 27*exp(6*x) - 60*exp(5*x) - 24*exp(4*x) + 155*exp(3*x) - 141*exp(2*x) + 50*exp(x) - 6)/4!.
%F G.f.: 5*x^4*(4+79*x-988*x^2-4414*x^3+52260*x^4-8721*x^5-374220*x^6) / ((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)*(1-7*x)*(1-9*x)*(1-11*x)*(1-15*x)). - _Colin Barker_, Oct 13 2017
%t With[{nmax = 50}, CoefficientList[Series[(Exp[15*x] - 12*Exp[11*x] + 24*Exp[9*x] - 14*Exp[7*x] + 27*Exp[6*x] - 60*Exp[5*x] - 24*Exp[4*x] + 155*Exp[3*x] - 141*Exp[2*x] + 50*Exp[x] - 6)/4!, {x, 0, nmax}], x] Range[0, nmax]!] (* _G. C. Greubel_, Oct 07 2017 *)
%o (PARI) x='x+O('x^50); concat([0,0,0,0], Vec(serlaplace((exp(15*x) -12*exp(11*x) +24*exp(9*x) -14*exp(7*x) +27*exp(6*x) -60*exp(5*x) -24*exp(4*x) +155*exp(3*x) -141*exp(2*x) +50*exp(x) -6)/4!))) \\ _G. C. Greubel_, Oct 07 2017
%o (PARI) concat(vector(4), Vec(5*x^4*(4+79*x-988*x^2-4414*x^3+52260*x^4-8721*x^5-374220*x^6) / ((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)*(1-7*x)*(1-9*x)*(1-11*x)*(1-15*x)) + O(x^30))) \\ _Colin Barker_, Oct 13 2017
%Y Cf. A016269, A047707, A051112-A051118, A094033-A094037.
%K nonn,easy
%O 0,5
%A Goran Kilibarda, _Vladeta Jovovic_, Apr 22 2004
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