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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

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OFFSET

0,3

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.

FORMULA

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

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 *)

PROG

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

CROSSREFS

Cf. A007889.