A097852 - OEIS

A097852

Expansion of (1+x^15)/((1-x^2)*(1-x^4)*(1-x^6)*(1-x^10)).

1, 0, 1, 0, 2, 0, 3, 0, 4, 0, 6, 0, 8, 0, 10, 1, 13, 1, 16, 2, 20, 3, 24, 4, 29, 6, 34, 8, 40, 10, 47, 13, 54, 16, 62, 20, 71, 24, 80, 29, 91, 34, 102, 40, 114, 47, 127, 54, 141, 62, 156, 71, 172, 80, 189, 91, 207, 102, 226, 114, 247, 127, 268, 141, 291, 156, 315, 172, 340, 189, 367

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OFFSET

0,5

COMMENTS

Poincare series for invariant polynomial functions on the space of binary forms of degree 6.

REFERENCES

Howe, Roger. "The Classical Groups" and invariants of binary forms, in The Mathematical Heritage of Hermann Weyl, Proc. Sympos. Pure Math., Amer. Math. Soc., Vol. 48 (1988): 133-166. See p. 164.

Sylvester, James Joseph, and Fabian Franklin. "Tables of the generating functions and groundforms for the binary quantics of the first ten orders." American Journal of Mathematics 2.3 (1879): 223-251.

Sylvester, James Joseph. "Tables of the generating functions and groundforms of the binary duodecimic, with some general remarks, and tables of the irreducible syzygies of certain quantics." American Journal of Mathematics 4.1 (1881): 41-61.

LINKS

Table of n, a(n) for n=0..70.

Andries Brouwer, Poincaré Series (See n=6).

J.-I. Igusa, Modular forms and projective invariants, Amer. J. Math., 89 (1967), 817-855; see p. 847.

R. P. Stanley, F. Zanello, Some asymptotic results on q-binomial coefficients, 2014.

Index entries for linear recurrences with constant coefficients, signature (-1,1,2,2,1,-1,-3,-3,-1,1,2,2,1,-1,-1).

MATHEMATICA

CoefficientList[Series[(1+x^15)/((1-x^2)(1-x^4)(1-x^6)(1-x^10)), {x, 0, 100}], x] (* Harvey P. Dale, Sep 29 2018 *)

CROSSREFS

For these Poincare series for d = 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20, 24 see A097852, A293933, A097851, A293934, A293935, A293936, A293937, A293938, A293939, A293940, A293941, A293942, A293943 respectively.

Sequence in context: A008821 A194749 A284969 * A008801 A073739 A223707

Adjacent sequences: A097849 A097850 A097851 * A097853 A097854 A097855

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 01 2004

STATUS

approved