OFFSET
0,3
COMMENTS
This is associated with the root system E8, and can be described using the additive function on the affine E8 diagram:
3
|
2--4--6--5--4--3--2--1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Arjeh M. Cohen and Robert L. Griess Jr., On finite simple subgroups of the complex Lie group of type E_8, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986), 367-405, Proc. Sympos. Pure Math., 47, Part 2, Amer. Math. Soc., Providence, RI, 1987.
Kaiwen Sun and Haowu Wang, Weyl invariant E8 Jacobi forms and E-strings, arXiv:2109.10578 [math.NT], 2021. See Table 1 p. 9.
Index entries for linear recurrences with constant coefficients, signature (1,2,0,-1,-4,-1,0,3,6,1,0,-4,-5,-5,0,5,5,4,0,-1,-6,-3,0,1,4,1,0,-2,-1,1).
FORMULA
G.f.: 1/((1-x)*(1-x^2)^2*(1-x^3)^2*(1-x^4)^2*(1-x^5)*(1-x^6)).
MAPLE
seq(coeff(series(1/((1-x)*(1-x^2)^2*(1-x^3)^2*(1-x^4)^2*(1-x^5)*(1-x^6)), x, n+1), x, n), n = 0..40); # G. C. Greubel, Jan 13 2020
MATHEMATICA
CoefficientList[Series[1/((1-x)(1-x^2)^2(1-x^3)^2(1-x^4)^2(1-x^5)(1-x^6)), {x, 0, 40}], x] (* Harvey P. Dale, Sep 16 2019 *)
PROG
(PARI) Vec(1/((1-x)*(1-x^2)^2*(1-x^3)^2*(1-x^4)^2*(1-x^5)*(1-x^6))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1-x)*(1-x^2)^2*(1-x^3)^2*(1-x^4)^2*(1-x^5)*(1-x^6)) )); // G. C. Greubel, Jan 13 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved