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 A266778 #14 Sep 08 2022 08:46:15
%S A266778 1,0,1,1,2,2,4,4,7,8,12,13,20,22,31,36,48,55,73,83,107,123,154,177,
%T A266778 220,251,306,351,422,481,575,652,771,875,1024,1158,1348,1518,1754,
%U A266778 1973,2265,2538,2901,3241,3684,4109,4646,5167,5823,6457,7246,8020,8965,9898,11031,12150,13495,14837,16428,18022,19905,21789,23999,26228,28813
%N A266778 Molien series for invariants of finite Coxeter group A_9.
%C A266778 The Molien series for the finite Coxeter group of type A_k (k >= 1) has g.f. = 1/Product_{i=2..k+1} (1-x^i).
%C A266778 Note that this is the root system A_k not the alternating group Alt_k.
%D A266778 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.
%H A266778 Ray Chandler, <a href="/A266778/b266778.txt">Table of n, a(n) for n = 0..1000</a>
%H A266778 <a href="/index/Rec#order_54">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 1, 1, 0, 0, -1, -1, -1, -1, -2, -1, 0, 1, 3, 3, 3, 2, 1, 0, -1, -4, -4, -4, -3, -2, 0, 2, 3, 4, 4, 4, 1, 0, -1, -2, -3, -3, -3, -1, 0, 1, 2, 1, 1, 1, 1, 0, 0, -1, -1, -1, 0, 1).
%H A266778 <a href="/index/Mo#Molien">Index entries for Molien series</a>
%F A266778 G.f.: 1/((1-t^2)*(1-t^3)*(1-t^4)*(1-t^5)*(1-t^6)*(1-t^7)*(1-t^8)*(1-t^9)*(1-t^10)).
%p A266778 seq(coeff(series( mul(1/(1-x^j), j=2..10), x, n+1), x, n), n = 0..70); # _G. C. Greubel_, Feb 02 2020
%t A266778 CoefficientList[Series[Product[1/(1-x^j), {j,2,10}], {x,0,70}], x] (* _G. C. Greubel_, Feb 02 2020 *)
%t A266778 LinearRecurrence[{0,1,1,1,0,0,-1,-1,-1,-1,-2,-1,0,1,3,3,3,2,1,0,-1,-4,-4,-4,-3,-2,0,2,3,4,4,4,1,0,-1,-2,-3,-3,-3,-1,0,1,2,1,1,1,1,0,0,-1,-1,-1,0,1},{1,0,1,1,2,2,4,4,7,8,12,13,20,22,31,36,48,55,73,83,107,123,154,177,220,251,306,351,422,481,575,652,771,875,1024,1158,1348,1518,1754,1973,2265,2538,2901,3241,3684,4109,4646,5167,5823,6457,7246,8020,8965,9898},70] (* _Harvey P. Dale_, Aug 10 2021 *)
%o A266778 (PARI) Vec( prod(j=2,10, 1/(1-x^j)) +O('x^70) ) \\ _G. C. Greubel_, Feb 02 2020
%o A266778 (Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( &*[1/(1-x^j): j in [2..10]] )); // _G. C. Greubel_, Feb 02 2020
%o A266778 (Sage)
%o A266778 def A266778_list(prec):
%o A266778 P.<x> = PowerSeriesRing(ZZ, prec)
%o A266778 return P( product(1/(1-x^j) for j in (2..10)) ).list()
%o A266778 A266778_list(70) # _G. C. Greubel_, Feb 02 2020
%Y A266778 Molien series for finite Coxeter groups A_1 through A_12 are A059841, A103221, A266755, A008667, A037145, A001996, and A266776-A266781.
%K A266778 nonn
%O A266778 0,5
%A A266778 _N. J. A. Sloane_, Jan 11 2016