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%I #23 Jun 23 2020 18:41:19
%S 1,11,71,351,1471,5503,18943,61183,187903,553983,1579007,4374527,
%T 11829247,31326207,81461247,208470015,525991935,1310457855,3228041215,
%U 7870611455,19012780031,45541752831,108246597631,255466668031,598980165631,1395931480063,3235049897983
%N Expansion of 1/((1-2*x)^5*(1-x)).
%C Occurs in the enumerations of inflations of code words babxxxdc [Albert et al. Sec 5.5.1]
%H M. H. Albert, M. D. Atkinson, R. Brignall, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i3p20">The enumeration of three pattern classes using monotone grid classes</a>, El. J. Combinat. 19 (3) (2012) P20.
%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 Santiago López de Medrano, <a href="https://arxiv.org/abs/2003.07508">On the genera of moment-angle manifolds associated to dual-neighborly polytopes, combinatorial formulas and sequences</a>, arXiv:2003.07508 [math.GT], 2020.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (11,-50,120,-160,112,-32).
%F a(n) = 2^n*(24+18*n+23*n^2+6*n^3+n^4)/12-1.
%F a(0)=1, a(1)=11, a(2)=71, a(3)=351, a(4)=1471, a(5)=5503, a(n)=11*a(n-1)- 50*a(n-2)+ 120*a(n-3)-160*a(n-4)+112*a(n-5)-32*a(n-6). - _Harvey P. Dale_, Mar 02 2015
%t CoefficientList[Series[1/((1-2x)^5(1-x)),{x,0,30}],x] (* or *) LinearRecurrence[ {11,-50,120,-160,112,-32},{1,11,71,351,1471,5503},30] (* _Harvey P. Dale_, Mar 02 2015 *)
%o (PARI) Vec(1/((1-2*x)^5*(1-x))+ O(x^30)) \\ _Michel Marcus_, Feb 12 2015
%Y Cf. A003472 (first differences).
%K nonn,easy
%O 0,2
%A _R. J. Mathar_, Feb 07 2013