A037145 Expansion of 1/((1-x^2)(1-x^3)...(1-x^6)).

1, 0, 1, 1, 2, 2, 4, 3, 6, 6, 9, 9, 14, 13, 19, 20, 26, 27, 36, 36, 47, 49, 60, 63, 78, 80, 97, 102, 120, 126, 149, 154, 180, 189, 216, 227, 260, 270, 307, 322, 361, 378, 424, 441, 492, 515, 568, 594, 656, 682, 750

Offset

0,5

Comments

Also, Molien series for invariants of finite Coxeter group A_5. The Molien series for the finite Coxeter group of type A_k (k >= 1) has G.f. = 1/Prod_{i=2..k+1} (1-x^i). - N. J. A. Sloane, Jan 11 2016

References

J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.

Links

Table of n, a(n) for n=0..50.

Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 1, 0, 0, -2, -2, -1, 0, 1, 2, 2, 0, 0, -1, -1, -1, 0, 1).

Mathematica

CoefficientList[Series[1/Times@@Table[(1-x^n), {n, 2, 6}], {x, 0, 50}], x] (* Harvey P. Dale, Dec 25 2012 *)

Crossrefs

Molien series for finite Coxeter groups A_1 through A_12 are A059841, A103221, A266755, A008667, A037145, A001996, and A266776-A266781.

Cf. A001402 (partial sums).

Sequence in context: A011754 A090105 A082146 * A341466 A357709 A238790

Adjacent sequences: A037142 A037143 A037144 * A037146 A037147 A037148

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved