A062206 a(n) = n^(2n).

1, 1, 16, 729, 65536, 9765625, 2176782336, 678223072849, 281474976710656, 150094635296999121, 100000000000000000000, 81402749386839761113321, 79496847203390844133441536, 91733330193268616658399616009, 123476695691247935826229781856256

Offset: 0

Author

Jason Earls, Jun 13 2001

Keywords

• easy
• nonn

Comments

a(n) is also the number of sequences of length 2n on n symbols. - Washington Bomfim, Oct 06 2009

a(n) is the number of endofunctions on [n] that map each even number to an even number and each odd number to an odd number. - Enrique Navarrete, Sep 30 2022

Links

• Winston de Greef, Table of n, a(n) for n = 0..213 (first 101 terms from Harry J. Smith)

Crossrefs

Cf. A062207, A086648, A155957.

Cf. A000290, A000312, A155955.

Cf. A085741, A212333.

Column k=0 of A245910 and A245980.

Programs

Mathematica

f[n_]:=n^(2*n); Join[{1},f[Range[20]]] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

PARI

a(n) = n^(2*n); \\ Harry J. Smith, Aug 02 2009

Python

def A062206(n): return n**(n<<1) # Chai Wah Wu, Nov 18 2022

Formula

a(n) = A000312(n)^2 = A000290(n)^n.

(-1)^n*determinant of the 2n X 2n matrix M_(i, j) = i+j if (i + j) is a multiple of n, M_(i, j) = 1 otherwise. - Benoit Cloitre, Aug 06 2003

a(n) = A155955(n,n) = A000290(A000312(n)). - Reinhard Zumkeller, Jan 31 2009

a(n) = n! * [x^n] 1/(1 + LambertW(-n*x)). - Ilya Gutkovskiy, Oct 03 2017

Sum_{n>=1} 1/a(n) = A086648. - Amiram Eldar, Nov 16 2020

Extensions

Initial term corrected by Reinhard Zumkeller, Jan 30 2009