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A022150 Coordination sequence for root lattice B_8.

%I A022150 #37 Sep 06 2023 01:36:50
%S A022150 1,128,3264,34624,216448,954880,3301952,9556160,24165120,54993792,
%T A022150 115021760,224533056,413862016,726758656,1224437056,1990370240,
%U A022150 3135895040,4806690432,7190192832,10524011840,15105409920,21301909504,29563091008,40433645248,54567743744
%N A022150 Coordination sequence for root lattice B_8.
%H A022150 Vincenzo Librandi, <a href="/A022150/b022150.txt">Table of n, a(n) for n = 0..1000</a>
%H A022150 M. Baake and U. Grimm, <a href="https://arxiv.org/abs/cond-mat/9706122">Coordination sequences for root lattices and related graphs</a>, arXiv:cond-mat/9706122, Zeit. f. Kristallographie, 212 (1997), 253-256.
%H A022150 R. Bacher, P. de la Harpe and B. Venkov, <a href="http://dx.doi.org/10.1016/S0764-4442(97)83542-2">Séries de croissance et séries d'Ehrhart associées aux réseaux de racines</a>, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
%H A022150 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A022150 a(0) = 1; for n > 0, a(n) = (3968*n^7 - 6720*n^6 + 35840*n^5 - 36960*n^4 + 60032*n^3 - 26880*n^2 + 11040*n)/315. - _Philippe Deléham_, Feb 20 2004
%F A022150 G.f.: (x^8 + 568*x^7 + 5852*x^6 + 18888*x^5 + 23750*x^4 + 12040*x^3 + 2268*x^2 + 120*x +1 )/(x -1)^8. - _Colin Barker_, Nov 18 2012
%t A022150 CoefficientList[Series[(x^8 + 568 x^7 + 5852 x^6 + 18888 x^5 + 23750 x^4 + 12040 x^3 + 2268 x^2 + 120 x + 1)/(x - 1)^8, {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 17 2013 *)
%o A022150 (Magma) [1] cat [(3968*n^7-6720*n^6+35840*n^5-36960*n^4+60032*n^3 -26880*n^2+11040*n)/315: n in [1..30]]; // _Vincenzo Librandi_, Oct 17 2013
%K A022150 nonn,easy
%O A022150 0,2
%A A022150 mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)