|
| |
|
|
A097852
|
|
Expansion of (1+x^15)/((1-x^2)*(1-x^4)*(1-x^6)*(1-x^10)).
|
|
13
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
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.
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
