A170965 Expansion of Product_{i=1..m} (1 + x^(4*i-1)) for m = 12.

1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 2, 1, 0, 1, 3, 1, 0, 2, 3, 1, 0, 3, 4, 1, 1, 4, 4, 1, 1, 5, 5, 1, 2, 7, 5, 1, 3, 8, 6, 0, 5, 10, 5, 1, 6, 12, 5, 1, 9, 13, 4, 2, 11, 14, 4, 3, 15, 15, 3, 5, 17, 15, 3, 7, 21, 15, 3, 10, 23, 15, 3, 13, 27, 14, 3, 17, 28, 13, 4, 21, 31, 12

Offset: 0

Author

N. J. A. Sloane, Aug 29 2010

Keywords

• nonn
• fini
• full
• easy

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.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..300 (full sequence)

Crossrefs

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

Programs

Mathematica

CoefficientList[Series[Product[1+x^(4i-1),{i,12}],{x,0,100}],x] (* Harvey P. Dale, Dec 24 2012 *)