This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A210068 #32 Sep 08 2022 08:46:01
%S A210068 1,2,6,12,25,44,79,128,208,318,483,704,1019,1430,1992,2712,3664,4862,
%T A210068 6407,8320,10735,13686,17344,21760,27153,33592,41353,50532,61468,
%U A210068 74290,89415,107008,127576,151332,178882,210496,246898,288420,335920
%N A210068 Expansion of 1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4)).
%C A210068 This is associated with the root system E7, and can be described using the additive function on the affine E7 diagram:
%C A210068 2
%C A210068 |
%C A210068 1--2--3--4--3--2--1
%H A210068 G. C. Greubel, <a href="/A210068/b210068.txt">Table of n, a(n) for n = 0..1000</a>
%H A210068 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (2, 2, -4, -3, 0, 7, 4, -5, -4, -5, 4, 7, 0, -3, -4, 2, 2, -1).
%F A210068 G.f.: 1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4)).
%p A210068 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
%t A210068 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 *)
%t A210068 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 *)
%o A210068 (Sage)
%o A210068 x=PowerSeriesRing(QQ,'x',40).gen()
%o A210068 1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4))
%o A210068 (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
%o A210068 (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
%Y A210068 For G2, the corresponding sequence is A001399.
%Y A210068 For F4, the corresponding sequence is A115264.
%Y A210068 For E6, the corresponding sequence is A164680.
%Y A210068 For E8, the corresponding sequence is A045513.
%K A210068 nonn,easy
%O A210068 0,2
%A A210068 _F. Chapoton_, Mar 17 2012