A170984 Expansion of (Product_{i=1..m-1} (1 + x^(4*i-1))) * (1 + x^(2*m-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, 2, 0, 1, 4, 1, 0, 2, 4, 1, 0, 4, 5, 1, 1, 5, 5, 1, 1, 7, 6, 1, 3, 9, 6, 0, 4, 11, 6, 0, 7, 13, 5, 1, 9, 15, 5, 2, 13, 16, 4, 3, 16, 17, 4, 5, 21, 18, 2, 8, 24, 17, 2, 12, 29, 16, 3, 16, 31, 15, 3, 21, 35, 13, 4, 27, 35, 11, 6, 33, 37

Offset: 0

Author

N. J. A. Sloane, Aug 29 2010

Keywords

• nonn
• fini
• full
• easy

Comments

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

References

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

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..276

Programs

PARI

my(m=12, x='x+O('x^275)); Vec((1+x^(2*m-1))*prod(i=1, m-1, 1+x^(4*i-1))) \\ Jinyuan Wang, Mar 08 2020