A169993 Expansion of Product_{i=0..m-1} (1 + x^(2*i+1)) for m=10.

1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 7, 8, 9, 10, 9, 11, 12, 12, 12, 13, 15, 15, 15, 16, 18, 17, 17, 18, 20, 19, 19, 20, 21, 21, 20, 21, 22, 22, 20, 22, 22, 21, 20, 21, 21, 20, 19, 19, 20, 18, 17, 17, 18, 16, 15, 15, 15, 13, 12, 12, 12, 11, 9, 10, 9, 8, 7, 7, 7, 6

Offset: 0

Author

N. J. A. Sloane, Aug 29 2010

Keywords

• nonn
• fini
• full
• easy

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 10 parts. Also, number of partitions of n into distinct odd parts not larger than 19. - Álvar Ibeas, Aug 01 2020

References

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

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..100 (full sequence)

Crossrefs

Cf. A000700, A169987, A169988, A169989, A169990, A169991, A169992, A169994, A169995.

Formula

a(n) = a(100-n). - Rick L. Shepherd, Feb 24 2013