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A008489 Expansion of (1-x^7)/(1-x)^7. 3
1, 7, 28, 84, 210, 462, 924, 1715, 2996, 4977, 7924, 12166, 18102, 26208, 37044, 51261, 69608, 92939, 122220, 158536, 203098, 257250, 322476, 400407, 492828, 601685, 729092, 877338, 1048894, 1246420, 1472772, 1731009, 2024400, 2356431, 2730812, 3151484 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Coordination sequence for 6-dimensional cyclotomic lattice Z[zeta_7].

Growth series of the affine Weyl group of type A6. - 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

M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv math.CO/0508136.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

Equals binomial transform of [1, 6, 15, 20, 15, 6, 1, -1, 1, -1, 1,...] - Gary W. Adamson, Apr 29 2008

a(n) = 7*n*(35*n^2+84+n^4)/120, n>0. - R. J. Mathar, Mar 17 2011

G.f.: (x^6+x^5+x^4+x^3+x^2+x+1) / (x-1)^6. - Colin Barker, Mar 04 2015

PROG

(PARI) Vec((x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^6 + O(x^100)) \\ Colin Barker, Mar 04 2015

CROSSREFS

Sequence in context: A166322 A008499 A049018 * A023032 A278969 A000579

Adjacent sequences:  A008486 A008487 A008488 * A008490 A008491 A008492

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 19 22:28 EDT 2018. Contains 316378 sequences. (Running on oeis4.)