A008492 Expansion of (1-x^10) / (1-x)^10.

1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48620, 92377, 167950, 293875, 497200, 816475, 1305502, 2037970, 3113110, 4662515, 6858280, 9922627, 14139190, 19866145, 27551380, 37749910, 51143752, 68564485, 91018730, 119716795, 156104740, 201900127

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Growth series of the affine Weyl group of type A9. - Paul E. Gunnells, Jan 06 2017

References

• 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.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Programs

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

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

Maple

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

Mathematica

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 *)

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

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

Formula

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

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