A062971 a(n) = (2*n)^n.

1, 2, 16, 216, 4096, 100000, 2985984, 105413504, 4294967296, 198359290368, 10240000000000, 584318301411328, 36520347436056576, 2481152873203736576, 182059119829942534144, 14348907000000000000000, 1208925819614629174706176, 108428035605965932354207744

Offset: 0

Author

Jason Earls, Jul 23 2001

Keywords

• easy
• nonn

Comments

Shift n^n left n bits.

Also the number of input-closed output-Boolean Moore machines on n states. - David Spivak, Feb 14 2020

Examples

			n=3: 3^3 shifted three bits to the left is 216 because 3^3 in binary is: [1, 1, 0, 1, 1] and 216 in binary is: [1, 1, 0, 1, 1, 0, 0, 0].
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..100

Crossrefs

Column k=1 of A246070.

Cf. A019762 (2*e).

Programs

Maple

a:= n-> (2*n)^n: seq(a(n), n=0..15); # Zerinvary Lajos, Jan 01 2009

Mathematica

Join[{1}, Table[(2*n)^n, {n,1,50}]] (* G. C. Greubel, Nov 10 2017 *)

PARI

for(n=0, 20, print1(shift(n^n,n), ", "))

Formula

E.g.f.: -(2*x*e^(-W(-2*x)))/(W(-2*x)*(W(-2*x)+1)), W(x) is Lambert's function. - Vladimir Kruchinin, May 09 2013

E.g.f.: 1/(1 + LambertW(-2*x)). - Vaclav Kotesovec, Dec 21 2014

Limit_{n->oo} a(n+1)/(n*a(n)) = 2*e. - Stefano Spezia, Mar 13 2023

Extensions

New description from Vladeta Jovovic, Mar 08 2003