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

0,19

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

Prog

(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

Crossrefs

Sequence in context: A303903 A348515 A209318 * A114021 A239287 A305258

Adjacent sequences: A170981 A170982 A170983 * A170985 A170986 A170987

Keyword

nonn,fini,full,easy

Author

N. J. A. Sloane, Aug 29 2010

Status

approved