A170961 Expansion of Product_{i=1..m} (1 + x^(4*i-1)) for m = 8.

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, 0, 1, 4, 3, 0, 1, 5, 3, 0, 2, 6, 2, 0, 3, 6, 2, 0, 5, 6, 1, 1, 5, 6, 1, 1, 7, 5, 0, 2, 7, 4, 0, 3, 8, 3, 0, 4, 7, 2, 0, 5, 7, 1, 1, 6, 5, 1, 1, 6, 5, 0, 2, 6, 3, 0, 2, 6, 2, 0, 3, 5, 1, 0, 3, 4, 1, 0, 4, 3, 0

Offset

0,19

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..136 (full sequence)

Formula

a(n) = a(136-n). - Rick L. Shepherd, Mar 01 2013

Mathematica

CoefficientList[Series[Product[1+x^(4i-1), {i, 8}], {x, 0, 110}], x] (* Harvey P. Dale, Aug 22 2012 *)

Crossrefs

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

Sequence in context: A180714 A170959 A170960 * A170962 A170963 A170964

Adjacent sequences: A170958 A170959 A170960 * A170962 A170963 A170964

Keyword

nonn,fini,full,easy

Author

N. J. A. Sloane, Aug 29 2010

Status

approved