%I #27 Sep 08 2022 08:44:35
%S 1,8,36,120,330,792,1716,3432,6434,11432,19412,31704,50058,76728,
%T 114564,167112,238722,334664,461252,625976,837642,1106520,1444500,
%U 1865256,2384418,3019752,3791348,4721816,5836490,7163640,8734692,10584456,12751362,15277704
%N Expansion of (1-x^8) / (1-x)^8.
%C Growth series of the affine Weyl group of type A7. - _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="/A008490/b008490.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n) = (180 + 469*n^2 + 70*n^4 + n^6) / 90 for n>0. - _Colin Barker_, Jan 06 2017
%F E.g.f.: -1 + (180 + 540*x + 990*x^2 + 510*x^3 + 135*x^4 + 15*x^5 + x^6)*exp(x)/90. - _G. C. Greubel_, Nov 07 2019
%p 1, seq((180+469*n^2+70*n^4+n^6)/90, n=1..40); # _G. C. Greubel_, Nov 07 2019
%t CoefficientList[Series[(1-x^8)/(1-x)^8,{x,0,40}],x] (* or *) LinearRecurrence[ {7,-21,35,-35,21,-7,1}, {1,8,36,120,330,792,1716, 3432}, 40] (* _Harvey P. Dale_, Jun 01 2019 *)
%o (PARI) Vec((1-x^8) / (1-x)^8 + O(x^50)) \\ _Colin Barker_, Jan 06 2017
%o (Magma) [1] cat [(180+469*n^2+70*n^4+n^6)/90: n in [1..40]]; // _G. C. Greubel_, Nov 07 2019
%o (Sage) [1]+[(180+469*n^2+70*n^4+n^6)/90 for n in (1..40)] # _G. C. Greubel_, Nov 07 2019
%o (GAP) Concatenation([1], List([1..40], n-> (180+469*n^2+70*n^4+n^6)/90 )); # _G. C. Greubel_, Nov 07 2019
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_