A037145 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(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/Product_{i=2..k+1} (1-x^i). - N. J. A. Sloane, Jan 11 2016

a(n) is the number of partitions of n into parts 2, 3, 4, 5, and 6. - Joerg Arndt, Apr 21 2026

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).

Formula

a(n) = floor((n^4+40*n^3+600*n^2+3680*n+17280)/17280 - (n mod 2)*(n+2)*(n+18)/192 + ((n+2) mod 3)*n/54). - Hoang Xuan Thanh, Apr 20 2026

Mathematica

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

Prog

(PARI) Vec(1/prod(k=2, 6, 1-x^k) + O(x^80)) \\ Hoang Xuan Thanh, Apr 20 2026

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: A090105 A082146 A391231 * A341466 A357709 A238790

Adjacent sequences: A037142 A037143 A037144 * A037146 A037147 A037148

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved