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%I #24 Sep 08 2022 08:45:02
%S 0,6,72,702,6480,58806,530712,4780782,43040160,387400806,3486725352,
%T 31380882462,282429005040,2541864234006,22876787671992,
%U 205891117745742,1853020145805120,16677181570526406,150094634909578632,1350851716510730622,12157665455570144400
%N J_n(9) (see A059379).
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.
%H Vincenzo Librandi, <a href="/A059410/b059410.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-27).
%F a(n) = 9^n - 3^n; a(n) = 12*a(n-1) - 27*a(n-2) for n > 1. - _Vincenzo Librandi_, Jun 03 2011
%F a(n) = 3^n*(3^n-1) = A000244(n) * A024023(n). - _Vincenzo Librandi_, Oct 04 2014
%F G.f.: 6*x/((1-3*x)*(1-9*x)). - _Vincenzo Librandi_, Oct 04 2014
%F a(n) = 6*A016142(n). - _R. J. Mathar_, Nov 23 2018
%p A059410:=n->9^n-3^n: seq(A059410(n), n=0..30); # _Wesley Ivan Hurt_, Aug 16 2016
%t Table[9^n - 3^n, {n, 0, 25}] (* or *) CoefficientList[Series[6 x /((1 - 3 x) (1 - 9 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 04 2014 *)
%o (Magma) [9^n-3^n: n in [0..20]]; // _Vincenzo Librandi_, Jun 03 2011
%Y Cf. A000244, A024023, A059379, A059380, A059409.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jan 30 2001
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