%I #26 Sep 08 2022 08:44:35
%S 1,9,45,165,495,1287,3003,6435,12870,24309,43749,75537,125805,202995,
%T 318483,487311,729036,1068705,1537965,2176317,3032523,4166175,5649435,
%U 7568955,10027986,13148685,17074629,21973545,28040265,35499915,44611347,55670823,69015960
%N Expansion of (1-x^9 ) / (1-x)^9.
%C Growth series of the affine Weyl group of type A8. - _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="/A008491/b008491.txt">Table of n, a(n) for n = 0..1000</a>
%H <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 a(n) = n*(3044 + 1869*n^2 + 126*n^4 + n^6)/560 for n>0. - _Colin Barker_, Jan 06 2017
%F E.g.f.: 1 + x*(5040 + 7560*x + 5320*x^2 + 1610*x^3 + 266*x^4 + 21*x^5 + x^6)*exp(x)/560. - _G. C. Greubel_, Nov 07 2019
%p 1, seq(n*(3044+1869*n^2+126*n^4+n^6)/560, n=1..40); # _G. C. Greubel_, Nov 07 2019
%t CoefficientList[Series[(1-x^9)/(1-x)^9,{x,0,35}],x] (* _Harvey P. Dale_, May 04 2014 *)
%o (PARI) Vec((1-x^9 )/(1-x)^9 + O(x^35)) \\ _Colin Barker_, Jan 06 2017
%o (Magma) [1] cat [n*(3044+1869*n^2+126*n^4+n^6)/560: n in [1..40]]; // _G. C. Greubel_, Nov 07 2019
%o (Sage) [1]+[n*(3044+1869*n^2+126*n^4+n^6)/560 for n in (1..40)] # _G. C. Greubel_, Nov 07 2019
%o (GAP) Concatenation([1], List([1..40], n-> n*(3044+1869*n^2+126*n^4+n^6)/560 )); # _G. C. Greubel_, Nov 07 2019
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_