|
|
A169987
|
|
Expansion of Product_{i=0..m-1} (1 + x^(2*i+1)) for m=4.
|
|
14
|
|
|
1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,9
|
|
COMMENTS
|
Product_{i=0..m-1} (1 + x^(2*i+1)) is the Poincaré polynomial for GL(m).
Number of self-conjugate partitions of n into at most 4 parts. Also, number of partitions of n into distinct odd parts not larger than 7. - Álvar Ibeas, Jul 30 2020
|
|
REFERENCES
|
H. Weyl, The Classical Groups, Princeton, 1946, see p. 233.
|
|
LINKS
|
|
|
MAPLE
|
f:=proc(m) local x, t1; t1:=mul((1+x^(2*i+1)), i=0..m-1); series(expand(t1), x, 200); end;
g:=m->seriestolist(f(m)); g(4);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,fini,full
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|