A169989 Expansion of Product_{i=0..m-1} 1 + x^(2*i+1) for m=6.

1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 2, 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 6 parts. Also, number of partitions of n into distinct odd parts not larger than 11. - Álvar Ibeas, Jul 30 2020

References

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

Crossrefs

Cf. A169987-A169995, A000700.

Programs

Mathematica

CoefficientList[Series[Product[1+x^(2i+1),{i,0,5}],{x,0,40}],x] (* Harvey P. Dale, Mar 03 2013 *)