OFFSET
0,2
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).
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
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 *)
PROG
(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
(Magma) [1] cat [(n^4+15*n^2+8)/4: n in [1..50]]; // G. C. Greubel, Nov 07 2019
(Sage) [1]+[(n^4+15*n^2+8)/4 for n in (1..50)] # G. C. Greubel, Nov 07 2019
(GAP) Concatenation([1], List([1..50], n-> (n^4+15*n^2+8)/4 )); # G. C. Greubel, Nov 07 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved