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%I #31 Sep 08 2022 08:44:50
%S 1,1,5,6,15,19,35,44,69,85,121,146,195,231,295,344,425,489,589,670,
%T 791,891,1035,1156,1325,1469,1665,1834,2059,2255,2511,2736,3025,3281,
%U 3605,3894,4255,4579,4979,5340,5781,6181,6665,7106,7635
%N Expansion of Molien series for 4-D extraspecial group 2^{1+2*2}.
%H Vincenzo Librandi, <a href="/A030533/b030533.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F G.f.: (x^8-x^6+2*x^4-x^2+1)/(1+x^2)^2/(-1+x^2)^2/(1+x)^2/(-1+x)^2 (not simplified).
%F G.f.: (x^2-x+1)*(x^2+1) / ((x-1)^4*(x+1)^2). [_Colin Barker_, Jan 31 2013]
%F a(n) = n*(2*n^2-9*(-1)^n+13)/24. [_Bruno Berselli_, Jan 31 2013]
%e 1+x^2+5*x^4+6*x^6+15*x^8+19*x^10+35*x^12+44*x^14+69*x^16+...
%t CoefficientList[Series[(x^2 - x + 1) (x^2 + 1)/((x - 1)^4 (x + 1)^2), {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 19 2013 *)
%t LinearRecurrence[{2,1,-4,1,2,-1},{1,1,5,6,15,19},50] (* _Harvey P. Dale_, May 05 2022 *)
%o (PARI) select(n->n,Vec((x^8-x^6+2*x^4-x^2+1)/(1+x^2)^2/(-1+x^2)^2/(1+x)^2/(-1+x)^2+O(x^99))) \\ _Charles R Greathouse IV_, Sep 24 2012
%o (Magma) [(n+1)*(2*n^2+4*n+15+9*(-1)^n)/24: n in [0..50]]; // _Vincenzo Librandi_, Oct 19 2013
%Y Cf. A014095, A030535, A030536, A030537.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_.
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