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%I #18 Feb 27 2020 11:47:11
%S 1,9,52,246,1039,4083,15274,55152,193957,668397,2266816,7589418,
%T 25143355,82571751,269173078,871958244,2809322833,9008574945,
%U 28768068460,91532284830,290283189991,917912770779,2894936303362
%N Fourth right hand column of triangle A163940.
%H G. C. Greubel, <a href="/A163941/b163941.txt">Table of n, a(n) for n = 0..1000</a>
%H Harry Crane, <a href="https://ajc.maths.uq.edu.au/pdf/61/ajc_v61_p057.pdf">Left-right arrangements, set partitions, and pattern avoidance</a>, Australasian Journal of Combinatorics, 61(1) (2015), 57-72.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9,-29,39,-18).
%F G.f.: 1/((1-x)*(1-2*x)*(1-3*x)^2).
%F a(n) = (1/4)*(2^(n+5) + (2*n - 3)*3^(n+2) - 1).
%F a(n) = 9*a(n-1) - 29*a(n-2) + 39*a(n-3) - 18*a(n-4).
%F E.g.f.: (1/4)*(32*exp(2*x) + 27*(2*x-1)*exp(3*x) - exp(x)). - _G. C. Greubel_, Aug 13 2017
%t LinearRecurrence[{9,-29,39,-18},{1,9,52,246},30] (* or *) CoefficientList[ Series[1/((1-x)(1-2x)(1-3x)^2),{x,0,30}],x] (* _Harvey P. Dale_, Aug 14 2011 *)
%o (PARI) Vec(1/((1-x)*(1-2*x)*(1-3*x)^2) + O(x^30)) \\ _Michel Marcus_, Feb 12 2015
%Y Equals the fourth right hand column of A163940.
%Y A163942 is another right hand column.
%K easy,nonn
%O 0,2
%A _Johannes W. Meijer_, Aug 13 2009
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