A062971 - OEIS

%I #56 Mar 13 2023 07:22:05

%S 1,2,16,216,4096,100000,2985984,105413504,4294967296,198359290368,

%T 10240000000000,584318301411328,36520347436056576,2481152873203736576,

%U 182059119829942534144,14348907000000000000000,1208925819614629174706176,108428035605965932354207744

%N a(n) = (2*n)^n.

%C Shift n^n left n bits.

%C Also the number of input-closed output-Boolean Moore machines on n states. - _David Spivak_, Feb 14 2020

%H Harry J. Smith, <a href="/A062971/b062971.txt">Table of n, a(n) for n = 0..100</a>

%F 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

%F E.g.f.: 1/(1 + LambertW(-2*x)). - _Vaclav Kotesovec_, Dec 21 2014

%F Limit_{n->oo} a(n+1)/(n*a(n)) = 2*e. - _Stefano Spezia_, Mar 13 2023

%e 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].

%p a:= n-> (2*n)^n: seq(a(n), n=0..15); # _Zerinvary Lajos_, Jan 01 2009

%t Join[{1}, Table[(2*n)^n, {n,1,50}]] (* _G. C. Greubel_, Nov 10 2017 *)

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

%Y Column k=1 of A246070.

%Y Cf. A019762 (2*e).

%K easy,nonn

%O 0,2

%A _Jason Earls_, Jul 23 2001

%E New description from _Vladeta Jovovic_, Mar 08 2003