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 A266774 #9 Sep 08 2022 08:46:15 %S A266774 1,0,1,0,2,0,3,0,5,0,7,1,11,1,15,2,22,3,30,5,42,7,56,11,76,15,99,22, %T A266774 131,30,169,42,219,56,278,76,355,99,445,131,560,169,695,219,863,278, %U A266774 1060,355,1303,445,1586,560,1930,695,2331,863,2812,1060,3370,1303,4035,1586,4802,1930,5708,2331,6751,2812,7972,3370,9373,4035,11004 %N A266774 Molien series for invariants of finite Coxeter group D_11. %C A266774 The Molien series for the finite Coxeter group of type D_k (k >= 3) has G.f. = 1/Prod_i (1-x^(1+m_i)) where the m_i are [1,3,5,...,2k-3,k-1]. If k is even only even powers of x appear, and we bisect the sequence. %D A266774 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59. %H A266774 G. C. Greubel, <a href="/A266774/b266774.txt">Table of n, a(n) for n = 0..1000</a> %H A266774 <a href="/index/Mo#Molien">Index entries for Molien series</a> %F A266774 G.f.: 1/((1-t^2)*(1-t^4)*(1-t^6)*(1-t^8)*(1-t^10)*(1-t^11)*(1-t^12)*(1-t^14)*(1-t^16)*(1-t^18)*(1-t^20)). %p A266774 seq(coeff(series(1/((1-x^11)*mul(1-x^(2*j), j=1..10)), x, n+1), x, n), n = 0..80); # _G. C. Greubel_, Feb 03 2020 %t A266774 CoefficientList[Series[1/((1-x^11)*Product[1-x^(2*j), {j,10}]), {x,0,80}], x] (* _G. C. Greubel_, Feb 03 2020 *) %o A266774 (PARI) Vec(1/((1-x^11)*prod(j=1,10,1-x^(2*j))) +O('x^80)) \\ _G. C. Greubel_, Feb 03 2020 %o A266774 (Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x^11)*(&*[1-x^(2*j): j in [1..10]])) )); // _G. C. Greubel_, Feb 03 2020 %o A266774 (Sage) %o A266774 def A266774_list(prec): %o A266774 P.<x> = PowerSeriesRing(ZZ, prec) %o A266774 return P( 1/((1-x^11)*product(1-x^(2*j) for j in (1..10))) ).list() %o A266774 A266774_list(80) # _G. C. Greubel_, Feb 03 2020 %Y A266774 Molien series for finite Coxeter groups D_3 through D_12 are A266755, A266769, A266768, A003402, and A266770-A266775. %K A266774 nonn %O A266774 0,5 %A A266774 _N. J. A. Sloane_, Jan 11 2016