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A094736 Number of connected 4-element multiantichains on a labeled n-set.

%I A094736 #11 May 26 2016 12:06:41
%S A094736 0,1,1,13,189,3816,88646,2013383,42040699,807900526,14537331816,
%T A094736 249111237453,4119281678909,66371933499236,1049372070568186,
%U A094736 16362812045380723,252561404639492319,3869204360738213946,58948921926491795756,894453362388005059193
%N A094736 Number of connected 4-element multiantichains on a labeled n-set.
%H A094736 Colin Barker, <a href="/A094736/b094736.txt">Table of n, a(n) for n = 0..850</a>
%F A094736 E.g.f.: (1/4!)*(exp(15*x) -12*exp(11*x) +24*exp(9*x) -2*exp(7*x) +27*exp(6*x) -132*exp(5*x) +12*exp(4*x) +359*exp(3*x) -501*exp(2*x) +314*exp(x)-90).
%F A094736 a(n) = (314-501*2^n+3*2^(2+2n)+359*3^n+2^n*3^(3+n)+8*3^(1+2n)-132*5^n-2*7^n-12*11^n+15^n)/24, n>0. - _Benedict W. J. Irwin_, May 25 2016
%F A094736 G.f.: x*(1-62*x +1651*x^2 -24816*x^3 +233562*x^4 -1431634*x^5 +5791471*x^6 -15717948*x^7 +28663875*x^8 -28066500*x^9) / ((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_, May 25 2016
%t A094736 Table[(314 - 501*2^n + 3*2^(2 + 2 n) + 359*3^n + 2^n*3^(3 + n) + 8*3^(1 + 2 n) - 132*5^n - 2*7^n - 12*11^n + 15^n)/ 24 (1 - UnitStep[-n]), {n, 0, 20}] (* _Benedict W. J. Irwin_, May 25 2016 *)
%o A094736 (PARI) concat(0, Vec(x*(1-62*x +1651*x^2 -24816*x^3 +233562*x^4 -1431634*x^5 +5791471*x^6 -15717948*x^7 +28663875*x^8 -28066500*x^9) / ((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^50))) \\ _Colin Barker_, May 25 2016
%Y A094736 Cf. A094033-A094037, A094729-A094738.
%K A094736 nonn,easy
%O A094736 0,4
%A A094736 Goran Kilibarda, _Vladeta Jovovic_, May 24 2004