A169987 Expansion of Product_{i=0..m-1} (1 + x^(2*i+1)) for m=4.

1, 1, 0, 1, 1, 1, 1, 1, 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 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.

Crossrefs

Cf. A169987-A169995 (these are all rows of the triangle in A178666), A000700.

Programs

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);

Mathematica

CoefficientList[Series[Product[1+x^(2i+1),{i,0,3}],{x,0,20}],x] (* Harvey P. Dale, Sep 15 2024 *)