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%I #21 Oct 09 2017 02:16:04
%S 0,1,1,8,75,796,8051,73788,623155,4965836,38028051,283400668,
%T 2072874035,14966280876,107083717651,761327161148,5388524417715,
%U 38017832427916,267623218488851,1880883687651228,13203904989574195,92616374066478956,649261556308773651
%N Number of connected 3-element multiantichains on a labeled n-set.
%H G. C. Greubel, <a href="/A094735/b094735.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (22,-190,820,-1849,2038,-840).
%F E.g.f.: (1/3!)*(exp(7*x) - 6*exp(5*x) + 3*exp(4*x) + 20*exp(3*x) - 39*exp(2*x) + 35*exp(x) - 14).
%F G.f.: -x*(1960*x^5 - 1695*x^4 + 731*x^3 - 176*x^2 + 21*x - 1) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(7*x-1)). - _Colin Barker_, Jul 13 2013
%F a(n) = (7^n - 6*5^n + 20*3^n + 3*4^n - 39*2^n + 35)/6, n > 0. - _Benedict W. J. Irwin_, May 25 2016
%t Table[(7^n-6*5^n+20*3^n+3*4^n-39*2^n+35)/6(1-UnitStep[-n]), {n, 0, 20}] (* _Benedict W. J. Irwin_, May 25 2016 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace((1/3!)*(exp(7*x) - 6*exp(5*x) + 3*exp(4*x) + 20*exp(3*x) - 39*exp(2*x) + 35*exp(x) - 14)))) \\ _G. C. Greubel_, Oct 08 2017
%Y Cf. A094033-A094037, A094729-A094738.
%K nonn,easy
%O 0,4
%A Goran Kilibarda, _Vladeta Jovovic_, May 24 2004
%E More terms from _Colin Barker_, Jul 13 2013
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