A170962 Expansion of Product_{i=1..m} (1 + x^(4*i-1)) for m = 9.

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, 0, 1, 5, 4, 0, 2, 7, 3, 0, 3, 7, 3, 0, 5, 8, 2, 1, 6, 8, 2, 1, 8, 8, 1, 2, 9, 7, 1, 3, 11, 7, 0, 5, 11, 5, 0, 6, 12, 4, 1, 8, 11, 3, 1, 9, 11, 2, 2, 11, 9, 1, 3, 11, 8, 1, 4, 12, 6, 0, 5, 11, 5

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..171 (full sequence)

Crossrefs

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

Formula

a(n) = a(171-n). - Rick L. Shepherd, Mar 01 2013