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%I #28 Sep 08 2022 08:44:36
%S 1,1,2,2,4,4,6,6,10,10,14,14,20,20,26,26,36,36,46,46,60,60,74,74,94,
%T 94,114,114,140,140,166,166,202,202,238,238,284,284,330,330,390,390,
%U 450,450,524,524,598,598
%N Molien series of 6 X 6 upper triangular matrices over GF( 2 ).
%C Different from A018819 (see g.f.). - _Joerg Arndt_, Apr 22 2016
%D D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.
%H G. C. Greubel, <a href="/A008645/b008645.txt">Table of n, a(n) for n = 0..1000</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=245">Encyclopedia of Combinatorial Structures 245</a>
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_63">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1).
%F G.f.: 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8)*(1-x^16)*(1-x^32)).
%p seq(coeff(series( 1/mul((1-x^(2^j)), j=0..5)), x, n+1), x, n), n = 0..50); # _G. C. Greubel_, Feb 02 2020
%t CoefficientList[Series[1/(1-x)/(1-x^2)/(1-x^4)/(1-x^8)/(1-x^16)/(1-x^32), {x, 0, 100}], x] (* _Vaclav Kotesovec_, Apr 22 2016 *)
%o (PARI) Vec( 1/prod(j=0,5, 1-x^(2^j)) +O('x^50) ) \\ _G. C. Greubel_, Feb 02 2020
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(&*[1-x^(2^j): j in [0..5]]) )); // _G. C. Greubel_, Feb 02 2020
%o (Sage)
%o def A008645_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( 1/product(1-x^(2^j) for j in (0..5)) ).list()
%o A008645_list(50) # _G. C. Greubel_, Feb 02 2020
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
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