A178795 - OEIS

A178795

Expansion of the polynomial (x^15-1)*(x^12-1)*(x^10-1)*(x^9-1)*(x^7-1)*(x^6-1)*(x^4-1)*(x-1) in increasing powers of x.

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

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OFFSET

0,13

COMMENTS

q^120*(q^30-1)*(q^24-1)*(q^20-1)*(q^18-1)*(q^14-1)*(q^12-1)*(q^8-1)*(q^2-1) is the order of the simple group E_8(q), if q is a prime power.

If f(x) is the x-polynomial and g(q) the q-polynomial, then g(q) = q^120*f(q^2). - Jean-François Alcover, Aug 25 2022

REFERENCES

R. L. Griess, Jr., Twelve Sporadic Groups, Springer, 1998; see p. 169.

LINKS

Table of n, a(n) for n=0..64.

Wikipedia, Lie group E8

EXAMPLE

With p=2 one gets the order of E_8(2): 337804753143634806261388190614085595079991692242467651576160959909068800000. - Jean-François Alcover, Aug 25 2022

PROG

(PARI) Vec((x^15-1)*(x^12-1)*(x^10-1)*(x^9-1)*(x^7-1)*(x^6-1)*(x^4-1)*(x-1)) \\ Michel Marcus, Aug 25 2022

CROSSREFS

Cf. A009968, A178779, A178780, A178781.

Sequence in context: A067627 A077233 A282290 * A123185 A133569 A141071

Adjacent sequences: A178792 A178793 A178794 * A178796 A178797 A178798

KEYWORD

sign,fini,full

AUTHOR

N. J. A. Sloane, Dec 26 2010

STATUS

approved