A170963 Expansion of Product_{i=1..m} (1 + x^(4*i-1)) for m = 10.

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, 0, 2, 7, 4, 0, 3, 8, 4, 0, 5, 9, 3, 1, 6, 10, 3, 1, 9, 10, 2, 2, 10, 10, 2, 3, 13, 10, 1, 5, 14, 9, 1, 7, 16, 8, 1, 9, 16, 7, 1, 11, 18, 5, 2, 14, 16, 4, 3, 16, 16, 3, 5, 18, 14

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..210 (full sequence)

Crossrefs

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

Formula

a(n) = a(210-n). - Rick L. Shepherd, Mar 01 2013