A169991 Expansion of Product_{i=0..m-1} (1 + x^(2*i+1)) for m=8.

1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 5, 4, 4, 5, 5, 6, 5, 6, 7, 7, 6, 7, 8, 7, 7, 7, 8, 7, 7, 7, 8, 7, 6, 7, 7, 6, 5, 6, 5, 5, 4, 4, 5, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 0, 1, 1

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 8 parts. Also, number of partitions of n into distinct odd parts not larger than 15. - Álvar Ibeas, Aug 01 2020

References

H. Weyl, The Classical Groups, Princeton, 1946, see p. 233.

Links

Table of n, a(n) for n=0..64.

Crossrefs

Cf. A000700, A169987, A169988, A169989, A169990, A169992, A169993, A169994, A169995.

Sequence in context: A121279 A123577 A005854 * A035435 A169992 A373535

Adjacent sequences: A169988 A169989 A169990 * A169992 A169993 A169994

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Aug 29 2010

Status

approved