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 A266770 #15 Sep 08 2022 08:46:15
%S A266770 1,0,1,0,2,0,3,1,5,1,7,2,11,3,15,5,21,7,28,11,38,15,49,21,65,28,82,38,
%T A266770 105,49,131,65,164,82,201,105,248,131,300,164,364,201,436,248,522,300,
%U A266770 618,364,733,436,860,522,1009,618,1175,733,1367,860,1579,1009,1824,1175,2093,1367,2400,1579,2738,1824,3120,2093,3539,2400,4011
%N A266770 Molien series for invariants of finite Coxeter group D_7.
%C A266770 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 A266770 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.
%H A266770 G. C. Greubel, <a href="/A266770/b266770.txt">Table of n, a(n) for n = 0..1000</a>
%H A266770 <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H A266770 <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1,0,0,1,0,-1,-1,-1,0,0,-2,0,0,1,1,0,1,2,1,0,1,-1, 0,-1,-2,-1,0,-1,-1,0,0,2,0,0,1,1,1,0,-1,0,0,-1,0,-1,0,1).
%F A266770 G.f.: 1/((1-x^2)*(1-x^4)*(1-x^6)*(1-x^7)*(1-x^8)*(1-x^10)*(1-x^12)).
%p A266770 seq(coeff(series(1/((1-x^7)*mul(1-x^(2*j), j=1..6)), x, n+1), x, n), n = 0..80); # _G. C. Greubel_, Jan 31 2020
%t A266770 CoefficientList[Series[1/((1-x^7)*Product[1-x^(2*j), {j,6}]), {x,0,80}], x] (* _G. C. Greubel_, Jan 31 2020 *)
%o A266770 (PARI) Vec(1/((1-x^7)*prod(j=1,6,1-x^(2*j))) +O('x^80)) \\ _G. C. Greubel_, Jan 31 2020
%o A266770 (Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x^7)*(&*[1-x^(2*j): j in [1..6]])) )); // _G. C. Greubel_, Jan 31 2020
%o A266770 (Sage)
%o A266770 def A266770_list(prec):
%o A266770 P.<x> = PowerSeriesRing(ZZ, prec)
%o A266770 return P( 1/((1-x^7)*product(1-x^(2*j) for j in (1..6))) ).list()
%o A266770 A266770_list(80) # _G. C. Greubel_, Jan 31 2020
%Y A266770 Molien series for finite Coxeter groups D_3 through D_12 are A266755, A266769, A266768, A003402, and A266770-A266775.
%K A266770 nonn
%O A266770 0,5
%A A266770 _N. J. A. Sloane_, Jan 10 2016