A170964 Expansion of Product_{i=1..m} (1 + x^(4*i-1)) for m = 11.

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, 0, 3, 8, 5, 0, 5, 10, 4, 1, 6, 11, 4, 1, 9, 12, 3, 2, 11, 12, 3, 3, 14, 13, 2, 5, 16, 12, 2, 7, 19, 12, 2, 10, 20, 11, 2, 12, 23, 10, 2, 16, 23, 8, 3, 19, 24, 7, 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..253 (full sequence)

Crossrefs

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

Programs

Mathematica

CoefficientList[Series[Product[1+x^(4k-1),{k,11}],{x,0,100}],x] (* Harvey P. Dale, Sep 19 2020 *)

Formula

a(n) = a(253-n). - Rick L. Shepherd, Mar 01 2013