A178779 - OEIS

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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

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OFFSET

0,20

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.

LINKS

Table of n, a(n) for n=0..26.

PROG

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

CROSSREFS

Cf. A008913, A178795.

Sequence in context: A276004 A133300 A337101 * A144451 A259287 A342592

Adjacent sequences: A178776 A178777 A178778 * A178780 A178781 A178782

KEYWORD

sign,fini,full,easy

AUTHOR

N. J. A. Sloane, Dec 26 2010

STATUS

approved