A008913 -id:A008913 - cp's OEIS frontend

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

Original entry on oeis.org

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

N. J. A. Sloane, Dec 26 2010

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

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

Cf. A008913, A178795.

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

A037249 a(n) = n^24(n^2-1)(n^6-1)(n^8-1)(n^12-1).

Original entry on oeis.org

0, 0, 3311126603366400, 5734420792816671844761600, 19009825523840945451297669120000, 2131486317725501953125000000000000000, 28289221506036457140036932327775928320000, 86325573304608766361629193317905069834240000

Offset: 0

N. J. A. Sloane

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Cf. A008913.

[n^24*(n^2-1)*(n^6-1)*(n^8-1)*(n^12-1): n in [0..10]]; // Vincenzo Librandi, Sep 14 2011

A037249:=n->n^24*(n^2-1)*(n^6-1)*(n^8-1)*(n^12-1): seq(A037249(n), n=0..10); # Wesley Ivan Hurt, Jan 28 2017

Table[n^24*(n^2 - 1) (n^6 - 1) (n^8 - 1) (n^12 - 1), {n, 0, 7}] (* Michael De Vlieger, Jan 30 2017 *)

a(n)=n^24*(n^2-1)*(n^6-1)*(n^8-1)*(n^12-1) \\ Charles R Greathouse IV, Jan 29 2017

cp's OEIS Frontend

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

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A037249 a(n) = n^24(n^2-1)(n^6-1)(n^8-1)(n^12-1).

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cp's OEIS Frontend

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

Views

Author

Keywords

Comments

References

Crossrefs

Programs

PARI

A037249 a(n) = n^24*(n^2-1)*(n^6-1)*(n^8-1)*(n^12-1).

Views

Author

Keywords

References

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

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

A037249 a(n) = n^24(n^2-1)(n^6-1)(n^8-1)(n^12-1).