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A210068
Expansion of 1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4)).
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
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
KEYWORD
nonn,easy
AUTHOR
F. Chapoton, Mar 17 2012
STATUS
approved