A062207 -id:A062207 - cp's OEIS frontend

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

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

Offset: 0

Jason Earls, Jun 13 2001

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

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

Cf. A062207, A086648, A155957.
Cf. A000290, A000312, A155955.
Cf. A085741, A212333.
Column k=0 of A245910 and A245980.

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

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

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

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

Initial term corrected by Reinhard Zumkeller, Jan 30 2009

A110931 Numbers k such that 2*k^k - 1 is prime.

Original entry on oeis.org

2, 3, 357, 1400, 205731, 296598

Offset: 1

Ray G. Opao, Sep 25 2005

a(5) > 4000. - Ray G. Opao, Oct 23 2014

a(5) > 101000. - Serge Batalov, Apr 13 2018

			3 is in the sequence since 2*3^3 - 1 = 53 is prime.

Numbers k such that b*k^k - b + 1 is prime: this sequence (b=2), A301521 (b=4), A302123 (b=6).

Cf. A110932, A062207, A108318.

[n: n in [0..500] | IsPrime(2*n^n-1)]; // Vincenzo Librandi, Nov 01 2014

Select[Range[1000], PrimeQ[2*#^# - 1] &] (* Vaclav Kotesovec, Oct 31 2014 *)

for(n=1,2000,1;if(isprime(2*n^n-1),print(n))) \\ Ray G. Opao, Oct 23 2014

a(5-6) from Ryan Propper, Jul 24-28 2022

A083282 a(n) = n^(3*n).

Original entry on oeis.org

1, 64, 19683, 16777216, 30517578125, 101559956668416, 558545864083284007, 4722366482869645213696, 58149737003040059690390169, 1000000000000000000000000000000, 23225154419887808141001767796309131

Offset: 1

Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Jun 02 2003

If sequence A000312 is used as the domain in the function f(n)=n^3, this sequence would be the resulting range. Also the range of the function f(n)=n^1.5 when sequence A062207 is used as the domain.

G. C. Greubel, Table of n, a(n) for n = 1..150

Cf. A000312, A062206, A062207, A089072.

[n^(3*n): n in [1..30]]; // G. C. Greubel, Nov 01 2022

Table[n^(3*n), {n, 30}] (* G. C. Greubel, Nov 01 2022 *)

[n^(3*n) for n in range(1,31)] # G. C. Greubel, Nov 01 2022

a(n) = A089072(3*n, n). - G. C. Greubel, Nov 01 2022

More terms from Michael Joseph Halm, May 16 2004

cp's OEIS Frontend

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

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A110931 Numbers k such that 2*k^k - 1 is prime.

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A083282 a(n) = n^(3*n).

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