A178696 Expansion of the polynomial (1+x^3)*(1+x^5)*(1+x^7)*(1+x^9)*(1+x^11)*(1+x^13)*(1+x^15)*(1+x^17)*(1+x^19).

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 5, 4, 7, 5, 7, 5, 8, 7, 8, 7, 9, 9, 8, 9, 9, 11, 8, 11, 9, 12, 9, 11, 10, 12, 10, 10, 12, 10, 11, 9, 12, 9, 11, 8, 11, 9, 9, 8, 9, 9, 7, 8, 7, 8, 5, 7, 5, 7, 4, 5, 5, 4, 4, 3, 4, 3, 3, 2, 3, 2, 2, 1, 2, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1

Offset

0,13

Comments

This is the Poincaré polynomial for the Lie group A_9.

References

Borel, A. and Chevalley, C., The Betti numbers of the exceptional groups, Mem. Amer. Math. Soc. 1955, no. 14, pp 1-9.

Links

Table of n, a(n) for n=0..99.

Mathematica

CoefficientList[Series[Times@@(1+x^(2*Range[9]+1)), {x, 0, 100}], x] (* Harvey P. Dale, Jul 09 2015 *)

Crossrefs

A row of A142724.

Sequence in context: A008624 A059169 A026922 * A161090 A349219 A178697

Adjacent sequences: A178693 A178694 A178695 * A178697 A178698 A178699

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Dec 25 2010

Status

approved