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A013499
a(n) = 2*n^n, n > 0, otherwise a(n) = 1.
6
1, 2, 8, 54, 512, 6250, 93312, 1647086, 33554432, 774840978, 20000000000, 570623341222, 17832200896512, 605750213184506, 22224013651116032, 875787780761718750, 36893488147419103232, 1654480523772673528354, 78692816150593075150848, 3956839311320627178247958, 209715200000000000000000000
OFFSET
0,2
COMMENTS
For n > 0, 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
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>0, resultant of x^n+1 and n*(x-1). - Ralf Stephan, Nov 20 2004
MATHEMATICA
lst={}; Do[AppendTo[lst, 2*n^n], {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
(Python)
def a(n): return 2 * n**n if n > 0 else 1
L = [a(n) for n in range(22)]; print(L) # Peter Luschny, May 09 2026
CROSSREFS
Cf. A007889.
Sequence in context: A052662 A375224 A365599 * A394078 A199576 A005155
KEYWORD
nonn,easy,changed
EXTENSIONS
Name edited by Michel Marcus, Jul 26 2017
Changed to a(1) = 2 by Peter Luschny, May 09 2026
STATUS
approved