OFFSET
0,2
COMMENTS
Computed with MAGMA using commands similar to those used to compute A161409.
REFERENCES
J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
N. Bourbaki, Groupes et algèbres de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..64
FORMULA
G.f. for B_m is the polynomial Product_{k=1..m} (1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.
MAPLE
seq(coeff(series(mul((1-x^(2*k))/(1-x), k=1..8), x, 65), x, n), n = 0 .. 64); # Muniru A Asiru, Oct 25 2018
MATHEMATICA
CoefficientList[Series[(1 - x^2) (1 - x^4) (1 - x^6) (1 - x^8) (1 - x^10) (1 - x^12) (1 - x^14) (1 - x^16) / (1 - x)^8, {x, 0, 70}], x] (* Vincenzo Librandi, Aug 22 2016 *)
PROG
(PARI) t='t+O('t^40); Vec(prod(k=1, 8, 1-t^(2*k))/(1-t)^8) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=40; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..8]])/(1-t)^8)); // G. C. Greubel, Oct 25 2018
CROSSREFS
KEYWORD
nonn,easy,fini,full
AUTHOR
John Cannon and N. J. A. Sloane, Nov 30 2009
STATUS
approved