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%I #37 Sep 08 2022 08:44:35
%S 1,11,66,286,1001,3003,8008,19448,43758,92378,184756,352715,646635,
%T 1144000,1960970,3267759,5308732,8428277,13103662,19986252,29952637,
%U 44167409,64159524,91914394,129984074,181618140,250918096,343018401,464297471,622622286
%N Expansion of (1-x^11) / (1-x)^11.
%C Coordination sequence for 10-dimensional cyclotomic lattice Z[zeta_11].
%C Growth series of the affine Weyl group of type A10. - _Paul E. Gunnells_, Jan 06 2017
%D R. Bott, The geometry and the representation theory of compact Lie groups, in: Representation Theory of Lie Groups, in: London Math. Soc. Lecture Note Ser., vol. 34, Cambridge University Press, Cambridge, 1979, pp. 65-90.
%H Colin Barker, <a href="/A008493/b008493.txt">Table of n, a(n) for n = 0..1000</a>
%H M. Beck and S. Hosten, <a href="https://arxiv.org/abs/math/0508136">Cyclotomic polytopes and growth series of cyclotomic lattices</a>, arXiv:math/0508136 [math.CO], 2005-2006.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F a(n) = A001287(n+10) - A001287(n-1). - _R. J. Mathar_, Aug 10 2013
%F a(n) = 11*n*(193248 + 152900*n^2 + 16401*n^4 + 330*n^6 + n^8)/362880 for n>0. - _Colin Barker_, Jan 06 2017
%F E.g.f.: 1 + x*(3991680 + 7983360*x + 7318080*x^2 + 3160080*x^3 + 765072*x^4 + 105336*x^5 + 8712*x^6 + 396*x^7 + 11*x^8)*exp(x)/362880. - _G. C. Greubel_, Nov 07 2019
%F a(n) = 10*a(n-1)-45*a(n-2)+120*a(n-3)-210*a(n-4)+252*a(n-5)-210*a(n-6)+120*a(n-7)-45*a(n-8)+10*a(n-9)-a(n-10). - _Wesley Ivan Hurt_, Jun 07 2021
%p 1, seq(11*n*(193248+152900*n^2+16401*n^4+330*n^6+n^8)/362880, n=1..40); # _G. C. Greubel_, Nov 07 2019
%t CoefficientList[(1-x^11)/(1-x)^11 + O[x]^30, x] (* _Jean-François Alcover_, Jan 09 2019 *)
%t Table[If[n==0,1, 11*n*(193248+152900*n^2+16401*n^4+330*n^6+n^8)/362880], {n,0,40}] (* _G. C. Greubel_, Nov 07 2019 *)
%o (PARI) Vec((1-x^11)/(1-x)^11 + O(x^40)) \\ _Colin Barker_, Jan 06 2017
%o (Magma) [1] cat [11*n*(193248+152900*n^2+16401*n^4+330*n^6+n^8)/362880: n in [1..40]]; // _G. C. Greubel_, Nov 07 2019
%o (Sage) [1]+[11*n*(193248+152900*n^2+16401*n^4+330*n^6+n^8)/362880 for n in (1..40)] # _G. C. Greubel_, Nov 07 2019
%o (GAP) Concatenation([1], List([1..40], n-> 11*n*(193248+152900*n^2 +16401*n^4 +330*n^6+n^8)/362880 )); # _G. C. Greubel_, Nov 07 2019
%Y Cf. A001287.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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