%I #69 Oct 23 2023 18:02:03
%S 1,1,16,729,65536,9765625,2176782336,678223072849,281474976710656,
%T 150094635296999121,100000000000000000000,81402749386839761113321,
%U 79496847203390844133441536,91733330193268616658399616009,123476695691247935826229781856256
%N a(n) = n^(2n).
%C a(n) is also the number of sequences of length 2n on n symbols. - _Washington Bomfim_, Oct 06 2009
%C 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
%H Winston de Greef, <a href="/A062206/b062206.txt">Table of n, a(n) for n = 0..213</a> (first 101 terms from Harry J. Smith)
%F a(n) = A000312(n)^2 = A000290(n)^n.
%F (-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
%F a(n) = A155955(n,n) = A000290(A000312(n)). - _Reinhard Zumkeller_, Jan 31 2009
%F a(n) = n! * [x^n] 1/(1 + LambertW(-n*x)). - _Ilya Gutkovskiy_, Oct 03 2017
%F Sum_{n>=1} 1/a(n) = A086648. - _Amiram Eldar_, Nov 16 2020
%t f[n_]:=n^(2*n); Join[{1},f[Range[20]]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2011 *)
%o (PARI) a(n) = n^(2*n); \\ _Harry J. Smith_, Aug 02 2009
%o (Python)
%o def A062206(n): return n**(n<<1) # _Chai Wah Wu_, Nov 18 2022
%Y Cf. A062207, A086648, A155957.
%Y Cf. A000290, A000312, A155955.
%Y Cf. A085741, A212333.
%Y Column k=0 of A245910 and A245980.
%K easy,nonn
%O 0,3
%A _Jason Earls_, Jun 13 2001
%E Initial term corrected by _Reinhard Zumkeller_, Jan 30 2009