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%I #27 Sep 17 2017 22:04:39
%S 1,3,9,33,165,1137,9837,95193,962541,9884889,102049197,1055383929,
%T 10921055661,113032307769,1169952636525,12109971475065,
%U 125349031354029,1297477519769145,13430093334225645,139013932289379321,1438923355509080877,14894194022848480185
%N Sum of values of vertices at level n of the hyperbolic Pascal pyramid.
%H Colin Barker, <a href="/A264237/b264237.txt">Table of n, a(n) for n = 0..987</a>
%H László Németh, <a href="http://arxiv.org/abs/1511.02067">Hyperbolic Pascal pyramid</a>, arXiv:1511.02067 [math.CO], 2015 (6th line of Table 2).
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (18,-99,226,-224,92,-12).
%F a(n) = 18*a(n-1) - 99*a(n-2) + 226*a(n-3) - 224*a(n-4) + 92*a(n-5) - 12*a(n-6), for n >= 7.
%F G.f.: -(20*x^5-8*x^4+58*x^3-54*x^2+15*x-1) / ((x-1)*(2*x^2-4*x+1)*(6*x^3-28*x^2+13*x-1)). - _Colin Barker_, Nov 09 2015
%t CoefficientList[Series[-(20*x^5 - 8*x^4 + 58*x^3 - 54*x^2 + 15*x - 1)/((x - 1)*(2*x^2 - 4*x + 1)*(6*x^3 - 28*x^2 + 13*x - 1)), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Sep 17 2017 *)
%o (PARI) Vec(-(20*x^5-8*x^4+58*x^3-54*x^2+15*x-1)/((x-1)*(2*x^2-4*x+1)*(6*x^3-28*x^2+13*x-1)) + O(x^30)) \\ _Colin Barker_, Nov 09 2015
%Y Cf. A035344, A264236.
%K nonn,easy
%O 0,2
%A _Michel Marcus_, Nov 09 2015
%E Definition edited by _Eric M. Schmidt_, Sep 17 2017
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