OFFSET
2,4
COMMENTS
Fn(z) is a rational function of degree -(n+1). Recently Brouwer, Cohen, and later Sally Jr. calculated Fn(z) for all n <= 18 and n = 20, 22, 24. It is rumored that Littelmann, Procesi, Laurent have calculated Fn(z) for many other values of n.
This sequence is somewhat badly defined. The values 18, 15, 48, 18 are not the degrees of the numerator of this rational function in lowest terms, but rather are degrees of a "representative" form. But there may be several representative forms with different degrees. - Andries E. Brouwer, Jan 15 2009
REFERENCES
Jean-Michel Kantor, Où en sont les mathématiques?, SMF, Vuibert, Chapitre 5, paragraphe 6, "Invariants des formes binaires : la formule de Cayley-Sylvester", pp. 73-74.
LINKS
Andries Brouwer, Poincaré Series.
A. E. Brouwer and A. M. Cohen, The Poincaré series of the polynomials invariant under SU2 in its irreducible representation of degree <=17, report ZW134, Math. Centr. Amsterdam, Dec. 1979.
J. J. Sylvester, Proof of the hitherto undemonstrated fundamental theorem of invariants, Phil. Mag. 30(5) (1878), 178-188.
J. J. Sylvester, Proof of the hitherto undemonstrated fundamental theorem of invariants, Phil. Mag. 30(5) (1878), 178-188.
EXAMPLE
F8(z) = (1 + z^8 + z^9 + z^10 + z^18)/Product_{i = 2..7} (1-z^i), hence a(8) = 18. (See A097851. - N. J. A. Sloane, Oct 02 2021)
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Benoit Cloitre, Feb 08 2003
STATUS
approved