OFFSET
0,2
COMMENTS
First differs from A161900 at index n=22. - Andrew Howroyd, Mar 17 2025
REFERENCES
N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche IV.)
J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
LINKS
FORMULA
The growth series for D_k is the polynomial f(k)*Product_{i=1..k-1} f(2*i), where f(m) = (1-x^m)/(1-x) [Corrected by N. J. A. Sloane, Aug 07 2021]. This is a row of the triangle in A162206.
MAPLE
# Growth series for D_k, truncated to terms of order M. - N. J. A. Sloane, Aug 07 2021
f := proc(m::integer) (1-x^m)/(1-x) ; end proc:
g := proc(k, M) local a, i; global f;
a:=f(k)*mul(f(2*i), i=1..k-1);
seriestolist(series(a, x, M+1));
end proc;
MATHEMATICA
f[m_] := (1-x^m)/(1-x);
With[{k = 22}, CoefficientList[f[k]*Product[f[2i], {i, 1, k-1}] + O[x]^k, x]] (* Jean-François Alcover, Feb 15 2023, after Maple code *)
CROSSREFS
Row 22 of A162206.
Growth series for groups D_n, n = 3,...,50: A161435, A162207, A162208, A162209, A162210, A162211, A162212, A162248, A162288, A162297, A162300, A162301, A162321, A162327, A162328, A162346, A162347, A162359, A162360, A162364, A162365, A162366, A162367, A162368, A162369, A162370, A162376, A162377, A162378, A162379, A162380, A162381, A162384, A162388, A162389, A162392, A162399, A162402, A162403, A162411, A162412, A162413, A162418, A162452, A162456, A162461, A162469, A162492.
KEYWORD
nonn,fini,full
AUTHOR
John Cannon and N. J. A. Sloane, Dec 01 2009
STATUS
approved