A008488 Expansion of (1-x^6) / (1-x)^6.

1, 6, 21, 56, 126, 252, 461, 786, 1266, 1946, 2877, 4116, 5726, 7776, 10341, 13502, 17346, 21966, 27461, 33936, 41502, 50276, 60381, 71946, 85106, 100002, 116781, 135596, 156606, 179976, 205877, 234486, 265986, 300566, 338421, 379752, 424766, 473676, 526701

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Growth series of the affine Weyl group of type A5. - Paul E. Gunnells, Dec 27 2016

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 (5,-10,10,-5,1).

Programs

GAP

Concatenation([1], List([1..50], n-> (n^4+15*n^2+8)/4 )); # G. C. Greubel, Nov 07 2019

Magma

[1] cat [(n^4+15*n^2+8)/4: n in [1..50]]; // G. C. Greubel, Nov 07 2019

Maple

1, seq((n^4+15*n^2+8)/4, n=1..50); # G. C. Greubel, Nov 07 2019

Mathematica

CoefficientList[Series[(1-x^6)/(1-x)^6,{x,0,30}],x] (* Harvey P. Dale, Sep 16 2016 *)

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

Sage

[1]+[(n^4+15*n^2+8)/4 for n in (1..50)] # G. C. Greubel, Nov 07 2019

Formula

Equals binomial transform of [1, 5, 10, 10, 5, 1, -1, 1, -1, 1, ...]. - Gary W. Adamson, May 12 2008

a(n) = (n^4 + 15*n^2 + 8)/4 for n > 0. - R. J. Mathar, Jan 27 2009

E.g.f.: -1 + (8 + 16*x + 22*x^2 + 6*x^3 + x^4)*exp(x)/4. - G. C. Greubel, Nov 07 2019