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Expansion of (1-x^10) / (1-x)^10.
3

%I #33 Sep 08 2022 08:44:35

%S 1,10,55,220,715,2002,5005,11440,24310,48620,92377,167950,293875,

%T 497200,816475,1305502,2037970,3113110,4662515,6858280,9922627,

%U 14139190,19866145,27551380,37749910,51143752,68564485,91018730,119716795,156104740,201900127

%N Expansion of (1-x^10) / (1-x)^10.

%C Growth series of the affine Weyl group of type A9. - _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="/A008492/b008492.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).

%F a(n) = (8064 + 26060*n^2 + 5985*n^4 + 210*n^6 + n^8) / 4032 for n>0. - _Colin Barker_, Jan 06 2017

%F E.g.f.: -1 + (8064 + 32256*x + 74592*x^2 + 55776*x^3 + 21336*x^4 + 4200*x^5 + 476*x^6 + 28*x^7 + x^8)*exp(x)/4032. - _G. C. Greubel_, Nov 07 2019

%p 1, seq((8064+26060*n^2+5985*n^4+210*n^6+n^8)/4032, n=1..40); # _G. C. Greubel_, Nov 07 2019

%t Table[If[n==0,1,(8064+26060*n^2+5985*n^4+210*n^6+n^8)/4032], {n,40}] (* _G. C. Greubel_, Nov 07 2019 *)

%o (PARI) Vec((1-x^10) / (1-x)^10 + O(x^40)) \\ _Charles R Greathouse IV_, Sep 26 2012, corrected by _Colin Barker_, Jan 06 2017

%o (Magma) [1] cat [(8064+26060*n^2+5985*n^4+210*n^6+n^8)/4032: n in [1..40]]; // _G. C. Greubel_, Nov 07 2019

%o (Sage) [1]+[(8064+26060*n^2+5985*n^4+210*n^6+n^8)/4032 for n in (1..40)] # _G. C. Greubel_, Nov 07 2019

%o (GAP) Concatenation([1], List([1..40], n-> (8064+26060*n^2+5985*n^4+ 210*n^6+n^8)/4032 )); # _G. C. Greubel_, Nov 07 2019

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_