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a(n) = 2*n^n, n >= 2, otherwise a(n) = 1.
4

%I #30 Jul 26 2017 07:52:55

%S 1,1,8,54,512,6250,93312,1647086,33554432,774840978,20000000000,

%T 570623341222,17832200896512,605750213184506,22224013651116032,

%U 875787780761718750,36893488147419103232,1654480523772673528354

%N a(n) = 2*n^n, n >= 2, otherwise a(n) = 1.

%C For n>=1, a(n) gives the number of alternating plane trees (trees such that the son of each vertex is ordered) on the set of vertices {1,2,..,n+1} (Chauve et al.). See A007889 for the non-ordered case. - _Peter Bala_, Aug 30 2011

%H Vincenzo Librandi, <a href="/A013499/b013499.txt">Table of n, a(n) for n = 0..300</a>

%H C. Chauve, S. Dulucq and A. Rechnitzer, <a href="https://doi.org/10.1006/jcta.2000.3121">Enumerating alternating trees</a>, J. Combin. Theory Ser. A 94 (2001), 142-151.

%H Frank Schmidt and Rodica Simion, <a href="https://doi.org/10.1007/BF01834201">Card shuffling and a transformation on S_n</a>, Aequationes Math. 44 (1992), no. 1, 11-34.

%F For n>1, resultant of x^n+1 and n(x-1). - _Ralf Stephan_, Nov 20 2004

%t lst={};Do[a=n^n;b=(n+1)^(n+1);ab=b-a;ba=b+a;AppendTo[lst,ba-ab],{n,4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Mar 20 2009 *)

%o (PARI) a(n) = if (n<=1, 1, 2*n^n); \\ _Michel Marcus_, Jul 26 2017

%Y Cf. A007889.

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E Name edited by _Michel Marcus_, Jul 26 2017