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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 (list; graph; refs; listen; history; text; internal format)
 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 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 *) 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:=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

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Last modified May 16 14:39 EDT 2021. Contains 343949 sequences. (Running on oeis4.)