|
%I #19 Mar 10 2020 21:40:09
%S 1,1,1,2,3,4,5,7,10,12,14,18,23,27,31,38,46,52,59,69,80,90,100,114,
%T 130,143,157,176,196,214,233,257,283,306,330,360,392,421,451,488,527,
%U 562,599,643,689,732,776,828,883,933,985,1046,1109,1168,1229,1299,1372,1440,1510
%N G.f.: (1+x)*(1+x^3)*(1+x^5)*(1+x^7)/((1-x^2)*(1-x^4)*(1-x^6)*(1-x^8)).
%C Poincaré series [or Poincare series] (or Molien series) for symmetric invariants in F_2(b_1, b_2, ... b_n) ⊗ E(e_1, e_2, ... e_n) with b_i 2-dimensional, e_i one-dimensional and the permutation action of S_n, in the case n=4.
%D A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 108.
%H Seiichi Manyama, <a href="/A089597/b089597.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (3,-5,8,-11,13,-15,16,-15,13,-11,8,-5,3,-1).
%F G.f.: (x^4-x^3+x^2-x+1)*(x^6-x^5+x^4-x^3+x^2-x+1) / ( (1+x+x^2)*(x^4+1)*(x^2+1)^2*(x-1)^4 ). - _R. J. Mathar_, Dec 18 2014
%F a(n)= +3*a(n-1) -5*a(n-2) +8*a(n-3) -11*a(n-4) +13*a(n-5) -15*a(n-6) +16*a(n-7) -15*a(n-8) +13*a(n-9) -11*a(n-10) +8*a(n-11) -5*a(n-12) +3*a(n-13) -a(n-14). - _R. J. Mathar_, Dec 18 2014
%t CoefficientList[Series[(1+x)*(1+x^3)*(1+x^5)*(1+x^7)/((1-x^2)*(1-x^4)*(1-x^6)*(1-x^8)), {x, 0, 70}], x] (* _Jinyuan Wang_, Mar 10 2020 *)
%o (PARI) Vec((1+x)*(1+x^3)*(1+x^5)*(1+x^7)/((1-x^2)*(1-x^4)*(1-x^6)*(1-x^8))+ O(x^100)) \\ _Michel Marcus_, Mar 19 2014
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Dec 31 2003
|
