A085534 a(n) = (2n)^(2n).

1, 4, 256, 46656, 16777216, 10000000000, 8916100448256, 11112006825558016, 18446744073709551616, 39346408075296537575424, 104857600000000000000000000, 341427877364219557396646723584, 1333735776850284124449081472843776, 6156119580207157310796674288400203776

Offset: 0

Author

N. J. A. Sloane, Jul 05 2003

Keywords

• nonn

Comments

All terms are both perfect squares and numbers of the form n^n. - William Boyles, Jul 31 2015

Intersection of A000290 and A000312. - Michel Marcus, Aug 04 2015

Intersection of A005843 and A000312. - Robert Israel, Aug 04 2015

The number of sequences of length 2n using 2n symbols. - Washington Bomfim, Jan 14 2020

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A000312, A073009, A083648, A085529.

Column k=0 of A246070.

Programs

Mathematica

{1}~Join~Table[(2 n)^(2 n), {n, 1, 4!}] (* Michael De Vlieger, Aug 04 2015 *)

Python

def A085534(n): return (m:=n<<1)**m # Chai Wah Wu, Nov 18 2022

Formula

a(n) = A000312(2*n). - Michel Marcus, Jul 31 2015

a(n) = A062971(n)^2. - Michel Marcus, Aug 04 2015

a(n) = [x^(2*n)] 1/(1 - 2*n*x). - Ilya Gutkovskiy, Oct 10 2017

Sum_{n>=0} 1/a(n) = 1 + (A073009-A083648)/2 = 1.2539277431... . - Amiram Eldar, May 17 2022