A170958 Expansion of Product_{i=1..m} (1 + x^(4*i-1)) for m = 5.

1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1

Offset: 0

Author

N. J. A. Sloane, Aug 29 2010

Keywords

• nonn
• fini
• full

Comments

Product_{i=1..m} (1 + x^(4*i-1)) is the Poincaré polynomial for both Sp(2m) and O(2m+1).

References

• H. Weyl, The Classical Groups, Princeton, 1946, see p. 238.

Crossrefs

Cf. A000700, A147599, A169975, A170956-A170965.

Programs

Mathematica

CoefficientList[Series[Product[1+x^(4i-1),{i,5}],{x,0,60}],x] (* Harvey P. Dale, Mar 09 2019 *)