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%I #28 Sep 08 2022 08:44:52
%S 0,6,72,648,5184,38880,279936,1959552,13436928,90699264,604661760,
%T 3990767616,26121388032,169789022208,1097098297344,7052774768640,
%U 45137758519296,287753210560512,1828079220031488,11577835060199424,73123168801259520,460675963447934976
%N a(n) = n*6^n.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-36).
%F a(n) = n * A000400(n). - _Michel Marcus_, Nov 09 2013
%F G.f.: 6*x/(1-6*x)^2. - _Vincenzo Librandi_, Apr 10 2016
%F a(n) = 12*a(n-1) - 36*a(n-2). - _Vincenzo Librandi_, Apr 10 2016
%F From _Amiram Eldar_, Jul 20 2020: (Start)
%F Sum_{n>=1} 1/a(n) = log(6/5).
%F Sum_{n>=1} (-1)^(n+1)/a(n) = log(7/6). (End)
%p A036292:=n->n*6^n; seq(A036292(n), n=0..50); # _Wesley Ivan Hurt_, Nov 09 2013
%t Table[n*6^n, {n,0,50}] (* _Wesley Ivan Hurt_, Nov 08 2013 *)
%t LinearRecurrence[{12, -36}, {0, 6}, 25] (* _Vincenzo Librandi_, Apr 10 2016 *)
%o (PARI) a(n) = n*6^n; \\ _Michel Marcus_, Nov 09 2013
%o (Magma) [n*6^n: n in [0..30]]; // _Vincenzo Librandi_, Apr 10 2016
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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