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A062971 a(n) = (2*n)^n. 12

%I

%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

%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->mul(2*sum(1, j=0..n), k=0..n): seq(a(n), n=-1..14);# _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,print(shift(n^n,n)))

%o (PARI) { for (n=0, 100, write("b062971.txt", n, " ", shift(n^n, n)) ) } \\ _Harry J. Smith_, Aug 14 2009

%Y Column k=1 of A246070.

%K easy,nonn

%O 0,2

%A _Jason Earls_, Jul 23 2001

%E New description from _Vladeta Jovovic_, Mar 08 2003

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Last modified February 25 19:39 EST 2021. Contains 341618 sequences. (Running on oeis4.)