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A045513 Expansion of 1/((1-x)*(1-x^2)^2*(1-x^3)^2*(1-x^4)^2*(1-x^5)*(1-x^6)). 4
1, 1, 3, 5, 10, 15, 27, 39, 63, 90, 135, 187, 270, 364, 505, 670, 902, 1173, 1545, 1976, 2550, 3218, 4081, 5083, 6357, 7825, 9659, 11772, 14366, 17342, 20956, 25080, 30031, 35667, 42357, 49945, 58881 (list; graph; refs; listen; history; text; internal format)
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

REFERENCES

Cohen, Arjeh M.; Griess, Robert L., 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.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

(sage) x=PowerSeriesRing(QQ, 'x', 40).gen()

1/((1-x)*(1-x^2)^2*(1-x^3)^2*(1-x^4)^2*(1-x^5)*(1-x^6))

(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

For G2, the corresponding sequence is A001399.

For F4, the corresponding sequence is A115264.

For E6, the corresponding sequence is A164680.

For E7, the corresponding sequence is A210068.

Sequence in context: A097513 A308932 A308997 * A326472 A326597 A008337

Adjacent sequences:  A045510 A045511 A045512 * A045514 A045515 A045516

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 2 17:02 EDT 2020. Contains 334787 sequences. (Running on oeis4.)