A169992 Expansion of Product_{i=0..m-1} (1 + x^(2*i+1)) for m=9.

1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 7, 6, 7, 8, 9, 8, 9, 10, 10, 10, 10, 12, 12, 11, 11, 13, 12, 12, 12, 13, 13, 12, 12, 12, 13, 11, 11, 12, 12, 10, 10, 10, 10, 9, 8, 9, 8, 7, 6, 7, 6, 5, 5, 5, 5, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 0, 1, 1

Offset: 0

Author

N. J. A. Sloane, Aug 29 2010

Keywords

• nonn
• fini
• full

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 9 parts. Also, number of partitions of n into distinct odd parts not larger than 17. - Álvar Ibeas, Aug 01 2020

References

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

Crossrefs

Cf. A000700, A169987, A169988, A169989, A169990, A169991, A169993, A169994, A169995.