A008490 Expansion of (1-x^8) / (1-x)^8.

1, 8, 36, 120, 330, 792, 1716, 3432, 6434, 11432, 19412, 31704, 50058, 76728, 114564, 167112, 238722, 334664, 461252, 625976, 837642, 1106520, 1444500, 1865256, 2384418, 3019752, 3791348, 4721816, 5836490, 7163640, 8734692, 10584456, 12751362, 15277704

Offset

0,2

Comments

Growth series of the affine Weyl group of type A7. - 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 (7,-21,35,-35,21,-7,1).

Formula

a(n) = (180 + 469*n^2 + 70*n^4 + n^6) / 90 for n>0. - Colin Barker, Jan 06 2017

E.g.f.: -1 + (180 + 540*x + 990*x^2 + 510*x^3 + 135*x^4 + 15*x^5 + x^6)*exp(x)/90. - G. C. Greubel, Nov 07 2019

Maple

1, seq((180+469*n^2+70*n^4+n^6)/90, n=1..40); # G. C. Greubel, Nov 07 2019

Mathematica

CoefficientList[Series[(1-x^8)/(1-x)^8, {x, 0, 40}], x] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {1, 8, 36, 120, 330, 792, 1716, 3432}, 40] (* Harvey P. Dale, Jun 01 2019 *)

Prog

(PARI) Vec((1-x^8) / (1-x)^8 + O(x^50)) \\ Colin Barker, Jan 06 2017
(Magma) [1] cat [(180+469*n^2+70*n^4+n^6)/90: n in [1..40]]; // G. C. Greubel, Nov 07 2019
(Sage) [1]+[(180+469*n^2+70*n^4+n^6)/90 for n in (1..40)] # G. C. Greubel, Nov 07 2019
(GAP) Concatenation([1], List([1..40], n-> (180+469*n^2+70*n^4+n^6)/90 )); # G. C. Greubel, Nov 07 2019

Crossrefs

Sequence in context: A051192 A008500 A306941 * A023033 A341205 A278971

Adjacent sequences: A008487 A008488 A008489 * A008491 A008492 A008493

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved