A008493 Expansion of (1-x^11) / (1-x)^11.

1, 11, 66, 286, 1001, 3003, 8008, 19448, 43758, 92378, 184756, 352715, 646635, 1144000, 1960970, 3267759, 5308732, 8428277, 13103662, 19986252, 29952637, 44167409, 64159524, 91914394, 129984074, 181618140, 250918096, 343018401, 464297471, 622622286

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Coordination sequence for 10-dimensional cyclotomic lattice Z[zeta_11].

Growth series of the affine Weyl group of type A10. - 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/0508136 [math.CO], 2005-2006.
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A001287.

Programs

GAP

Concatenation([1], List([1..40], n-> 11*n*(193248+152900*n^2 +16401*n^4 +330*n^6+n^8)/362880 )); # G. C. Greubel, Nov 07 2019

Magma

[1] cat [11*n*(193248+152900*n^2+16401*n^4+330*n^6+n^8)/362880: n in [1..40]]; // G. C. Greubel, Nov 07 2019

Maple

1, seq(11*n*(193248+152900*n^2+16401*n^4+330*n^6+n^8)/362880, n=1..40); # G. C. Greubel, Nov 07 2019

Mathematica

CoefficientList[(1-x^11)/(1-x)^11 + O[x]^30, x] (* Jean-François Alcover, Jan 09 2019 *)
Table[If[n==0,1, 11*n*(193248+152900*n^2+16401*n^4+330*n^6+n^8)/362880], {n,0,40}] (* G. C. Greubel, Nov 07 2019 *)

PARI

Vec((1-x^11)/(1-x)^11 + O(x^40)) \\ Colin Barker, Jan 06 2017

Sage

[1]+[11*n*(193248+152900*n^2+16401*n^4+330*n^6+n^8)/362880 for n in (1..40)] # G. C. Greubel, Nov 07 2019

Formula

a(n) = A001287(n+10) - A001287(n-1). - R. J. Mathar, Aug 10 2013

a(n) = 11*n*(193248 + 152900*n^2 + 16401*n^4 + 330*n^6 + n^8)/362880 for n>0. - Colin Barker, Jan 06 2017

E.g.f.: 1 + x*(3991680 + 7983360*x + 7318080*x^2 + 3160080*x^3 + 765072*x^4 + 105336*x^5 + 8712*x^6 + 396*x^7 + 11*x^8)*exp(x)/362880. - G. C. Greubel, Nov 07 2019

a(n) = 10*a(n-1)-45*a(n-2)+120*a(n-3)-210*a(n-4)+252*a(n-5)-210*a(n-6)+120*a(n-7)-45*a(n-8)+10*a(n-9)-a(n-10). - Wesley Ivan Hurt, Jun 07 2021