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%I #43 Sep 08 2022 08:44:35
%S 1,6,21,56,126,252,461,786,1266,1946,2877,4116,5726,7776,10341,13502,
%T 17346,21966,27461,33936,41502,50276,60381,71946,85106,100002,116781,
%U 135596,156606,179976,205877,234486,265986,300566,338421,379752,424766,473676,526701
%N Expansion of (1-x^6) / (1-x)^6.
%C Growth series of the affine Weyl group of type A5. - _Paul E. Gunnells_, Dec 27 2016
%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="/A008488/b008488.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F Equals binomial transform of [1, 5, 10, 10, 5, 1, -1, 1, -1, 1, ...]. - _Gary W. Adamson_, May 12 2008
%F a(n) = (n^4 + 15*n^2 + 8)/4 for n > 0. - _R. J. Mathar_, Jan 27 2009
%F E.g.f.: -1 + (8 + 16*x + 22*x^2 + 6*x^3 + x^4)*exp(x)/4. - _G. C. Greubel_, Nov 07 2019
%p 1, seq((n^4+15*n^2+8)/4, n=1..50); # _G. C. Greubel_, Nov 07 2019
%t CoefficientList[Series[(1-x^6)/(1-x)^6,{x,0,30}],x] (* _Harvey P. Dale_, Sep 16 2016 *)
%o (PARI) Vec((1-x^6) / (1-x)^6 + O(x^50)) \\ _Charles R Greathouse IV_, Sep 26 2012, corrected by _Colin Barker_, Jan 06 2017
%o (Magma) [1] cat [(n^4+15*n^2+8)/4: n in [1..50]]; // _G. C. Greubel_, Nov 07 2019
%o (Sage) [1]+[(n^4+15*n^2+8)/4 for n in (1..50)] # _G. C. Greubel_, Nov 07 2019
%o (GAP) Concatenation([1], List([1..50], n-> (n^4+15*n^2+8)/4 )); # _G. C. Greubel_, Nov 07 2019
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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