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%I #31 Apr 17 2022 08:23:20
%S 12,384,9216,196608,3932160,75497472,1409286144,25769803776,
%T 463856467968,8246337208320,145135534866432,2533274790395904,
%U 43910096366862336,756604737398243328,12970366926827028480,221360928884514619392,3763135791036748529664
%N a(n) = 3n*4^(2n-1).
%C a(n) is the number of spanning trees for the 2n-crossed prism graph with n >= 2.
%C Sequence extended to n=1 using the closed form.
%H Vincenzo Librandi, <a href="/A193132/b193132.txt">Table of n, a(n) for n = 1..300</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CrossedPrismGraph.html">Crossed Prism Graph</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SpanningTree.html">Spanning Tree</a>.
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (32,-256).
%F O.g.f.: 12*x/(16*x-1)^2.
%F a(n) = 32*a(n-1) - 256*a(n-2). - _Harvey P. Dale_, Apr 08 2015
%F From _Amiram Eldar_, Apr 17 2022: (Start)
%F a(n) = 3*A267796(n-1).
%F Sum_{n>=1} 1/a(n) = (4/3)*log(16/15).
%F Sum_{n>=1} (-1)^(n+1)/a(n) = (4/3)*log(17/16). (End)
%t LinearRecurrence[{32,-256},{12,384},20] (* _Harvey P. Dale_, Apr 08 2015 *)
%o (Magma) [3*n*4^(2*n-1): n in [1..20]]; // _Vincenzo Librandi_, Jul 17 2011
%o (PARI) a(n)=3*n<<(4*n-2) \\ _Charles R Greathouse IV_, Jul 30 2011
%Y Cf. A267796.
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Jul 16 2011
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