A178779 Expansion of the polynomial x^12*(x^6-1)*(x^4-1)*(x^3-1)*(x-1) in increasing powers of x.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, 1, -1, 2, -1, 1, 0, -1, 0, -1, 1

Offset: 0

Author

N. J. A. Sloane, Dec 26 2010

Keywords

• sign
• fini
• full
• easy

Comments

q^24*(q^12-1)*(q^8-1)*(q^6-1)*(q^2-1) is the order of the simple group F_4(q), if q is a prime power.

The x-polynomial f(x) and the q-polynomial g(q) are such that g(q) = f(q^2) - Jean-François Alcover, Aug 25 2022

References

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

Crossrefs

Cf. A008913, A178795.

Programs

PARI

Vecrev(x^12*(x^6-1)*(x^4-1)*(x^3-1)*(x-1)) \\ Michel Marcus, Aug 25 2022