A013499 a(n) = 2*n^n, n >= 2, otherwise a(n) = 1.

1, 1, 8, 54, 512, 6250, 93312, 1647086, 33554432, 774840978, 20000000000, 570623341222, 17832200896512, 605750213184506, 22224013651116032, 875787780761718750, 36893488147419103232, 1654480523772673528354

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• C. Chauve, S. Dulucq and A. Rechnitzer, Enumerating alternating trees, J. Combin. Theory Ser. A 94 (2001), 142-151.
• Frank Schmidt and Rodica Simion, Card shuffling and a transformation on S_n, Aequationes Math. 44 (1992), no. 1, 11-34.

Crossrefs

Cf. A007889.

Programs

Mathematica

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 *)

PARI

a(n) = if (n<=1, 1, 2*n^n); \\ Michel Marcus, Jul 26 2017

Formula

For n>1, resultant of x^n+1 and n(x-1). - Ralf Stephan, Nov 20 2004

Extensions

Name edited by Michel Marcus, Jul 26 2017