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%I #24 Aug 07 2023 11:14:06
%S 0,1,1,7,37,151,541,1807,5797,18151,55981,171007,519157,1569751,
%T 4733821,14250607,42850117,128746951,386634061,1160688607,3483638677,
%U 10454061751,31368476701,94118013007,282379204837,847187946151,2541664501741,7625194831807
%N Number of connected ordered 2-element multiantichains on a labeled n-set.
%H G. C. Greubel, <a href="/A094729/b094729.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F E.g.f.: exp(3*x) - 3*exp(2*x) + 4*exp(x) - 2.
%F From _Colin Barker_, Jul 07 2013: (Start)
%F a(n) = 4-3*2^n+3^n for n>0.
%F a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3) for n>3.
%F G.f.: x*(1 - 5*x + 12*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).
%F (End)
%t With[{nmax = 50}, CoefficientList[Series[Exp[3*x] - 3*Exp[2*x] + 4*Exp[x] - 2, {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Oct 06 2017 *)
%t LinearRecurrence[{6,-11,6},{0,1,1,7},30] (* _Harvey P. Dale_, Aug 07 2023 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace(exp(3*x)-3*exp(2*x) +4*exp(x)-2))) \\ _G. C. Greubel_, Oct 06 2017
%o (PARI) concat(0, Vec(x*(1 - 5*x + 12*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)) + O(x^30))) \\ _Colin Barker_, Oct 13 2017
%Y Cf. A094033-A094037, A094729-A094738.
%K nonn,easy
%O 0,4
%A Goran Kilibarda, _Vladeta Jovovic_, May 24 2004
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