%I #28 Sep 08 2022 08:44:35
%S 1,13,91,455,1820,6188,18564,50388,125970,293930,646646,1352078,
%T 2704156,5200299,9657687,17383769,30421300,51894115,86487037,
%U 141101961,225742452,354691350,548060110,833805154,1250325622,1849778840,2702274848,3901139736,5569469620
%N Expansion of (1-x^13) / (1-x)^13.
%C Coordination sequence for 12-dimensional cyclotomic lattice Z[zeta_13].
%H Colin Barker, <a href="/A008495/b008495.txt">Table of n, a(n) for n = 0..1000</a>
%H M. Beck and S. Hosten, <a href="http://arxiv.org/abs/math/0508136">Cyclotomic polytopes and growth series of cyclotomic lattices</a>, arXiv:math/0508136 [math.CO], 2005-2006.
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F From _Colin Barker_, Jan 06 2017: (Start)
%F a(n) = 13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800 for n>0.
%F G.f.: (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12) / (1 - x)^12. (End)
%F E.g.f.: 1 + x*(518918400 +1297296000*x +1470268800*x^2 +821620800*x^3 + 263783520*x^4 +51171120*x^5 +6280560*x^6 +489060*x^7 +24310*x^8 + 715*x^9 +13*x^10)*exp(x)/39916800. - _G. C. Greubel_, Nov 07 2019
%p 1, seq(13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800, n=1..40); # _G. C. Greubel_, Nov 07 2019
%t CoefficientList[(1-x^13)/(1-x)^13 + O[x]^30, x] (* _Jean-François Alcover_, Jan 09 2019 *)
%t Table[If[n==0,1,13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800], {n,0,40}] (* _G. C. Greubel_, Nov 07 2019 *)
%o (PARI) Vec((1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12) / (1 - x)^12 + O(x^30)) \\ _Colin Barker_, Jan 06 2017
%o (Magma) [1] cat [13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800: n in [1..40]]; // _G. C. Greubel_, Nov 07 2019
%o (Sage) [1]+[13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800 for n in (1..40)] # _G. C. Greubel_, Nov 07 2019
%o (GAP) Concatenation([1], List([1..40], n-> 13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800 )); # _G. C. Greubel_, Nov 07 2019
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_