A210068 Expansion of 1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4)).

1, 2, 6, 12, 25, 44, 79, 128, 208, 318, 483, 704, 1019, 1430, 1992, 2712, 3664, 4862, 6407, 8320, 10735, 13686, 17344, 21760, 27153, 33592, 41353, 50532, 61468, 74290, 89415, 107008, 127576, 151332, 178882, 210496, 246898, 288420, 335920

Offset

0,2

Comments

This is associated with the root system E7, and can be described using the additive function on the affine E7 diagram:

2

|

1--2--3--4--3--2--1

Links

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

Index entries for linear recurrences with constant coefficients, signature (2, 2, -4, -3, 0, 7, 4, -5, -4, -5, 4, 7, 0, -3, -4, 2, 2, -1).

Formula

G.f.: 1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4)).

Maple

seq(coeff(series(1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4)), x, n+1), x, n), n = 0 .. 40); # G. C. Greubel, Jan 13 2020

Mathematica

CoefficientList[Series[1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4)), {x, 0, 40}], x] (* G. C. Greubel, Jan 13 2020 *)
LinearRecurrence[{2, 2, -4, -3, 0, 7, 4, -5, -4, -5, 4, 7, 0, -3, -4, 2, 2, -1}, {1, 2, 6, 12, 25, 44, 79, 128, 208, 318, 483, 704, 1019, 1430, 1992, 2712, 3664, 4862}, 40] (* Harvey P. Dale, Sep 24 2021 *)

Prog

(Sage)
x=PowerSeriesRing(QQ, 'x', 40).gen()
1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4))
(PARI) Vec(1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4))+O(x^40)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4)) )); // 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 E8, the corresponding sequence is A045513.

Sequence in context: A175943 A228816 A294565 * A210633 A304710 A137829

Adjacent sequences: A210065 A210066 A210067 * A210069 A210070 A210071

Keyword

nonn,easy

Author

F. Chapoton, Mar 17 2012

Status

approved