A178665 Expansion of the polynomial (1+x^3)*(1+x^15)*(1+x^23)*(1+x^27)*(1+x^35)*(1+x^39)*(1+x^47)*(1+x^59).

1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 3, 0, 0, 2, 1, 0, 0, 1, 1, 1, 0, 1, 4, 0, 0, 4, 1, 0, 1, 1, 1, 0, 0, 2, 3, 0, 1, 5, 0, 0, 2, 1, 2, 0, 1, 4, 2, 0, 2, 5, 0, 0, 3, 0, 1, 0, 0, 5, 1, 0, 5, 4, 0, 1, 4, 1, 1, 1, 1, 5, 0, 0, 6, 2, 0, 2, 3, 1, 0, 1, 2, 4, 0, 1, 8, 1, 0, 4, 2, 1, 0, 1, 3, 2, 0, 2, 6, 0, 0, 5, 1, 1, 1, 1

Offset

0,39

Comments

This is the Poincaré polynomial for the Lie group E_8.

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..143.

Mathematica

CoefficientList[Series[Times@@Table[(1+x^e), {e, {3, 15, 23, 27, 35, 39, 47, 59}}], {x, 0, 150}], x] (* Harvey P. Dale, Oct 28 2025 *)

Crossrefs

Cf. A142724, A178600, A178602, A178580, A178651.

Sequence in context: A355682 A063933 A085860 * A170958 A178651 A046810

Adjacent sequences: A178662 A178663 A178664 * A178666 A178667 A178668

Keyword

nonn,fini

Author

N. J. A. Sloane, Dec 24 2010

Status

approved