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%I #17 Mar 09 2023 16:15:01
%S 1,14,121,834,5037,27918,145777,728858,3526933,16640262,76952793,
%T 350167122,1572467389,6984206846,30735634369,134202204426,
%U 582040933605,2509672804470,10766469841705,45982221941570,195609944400781
%N Fifth right hand column of triangle A163940.
%H G. C. Greubel, <a href="/A163942/b163942.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_05">Index entries for linear recurrences with constant coefficients</a>, signature (14,-75,190,-224,96).
%F G.f.: 1/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)^2).
%F a(n) = (1/18)*(3^(n+6) + (3*n-10)*4^(n+3) - 9*2^(n+3) + 1).
%F a(n) = 14*a(n-1) - 75*a(n-2) + 190*a(n-3) - 224*a(n-4) + 96*a(n-5).
%F E.g.f.: (1/18)*( 729*exp(3*x) + 128*(6*x-5)*exp(4*x) - 72*exp(2*x) + exp(x)). - _G. C. Greubel_, Aug 13 2017
%t CoefficientList[Series[1/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)^2), {x, 0, 50}], x] (* _G. C. Greubel_, Aug 13 2017 *)
%t LinearRecurrence[{14,-75,190,-224,96},{1,14,121,834,5037},30] (* _Harvey P. Dale_, Mar 09 2023 *)
%o (PARI) Vec(1/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)^2) + O(x^30)) \\ _Michel Marcus_, Feb 12 2015
%Y Equals the fifth right hand column of A163940.
%Y A163941 is another right hand column.
%K easy,nonn
%O 0,2
%A _Johannes W. Meijer_, Aug 13 2009
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