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%I #34 Feb 20 2023 08:02:09
%S 1,1,7,53,511,6249,93311,1647085,33554431,774840977,19999999999,
%T 570623341221,17832200896511,605750213184505,22224013651116031,
%U 875787780761718749,36893488147419103231,1654480523772673528353,78692816150593075150847,3956839311320627178247957
%N a(n) = 2*n^n-1.
%C Also: a(n) = 2m-1 where m is given by Sum_{i = 1..m } 2*i-1 = n^(2*n) (A062206).
%C "By setting n=m^p, one sees that m^(2p), an even power of any integer, is equal to the sum of all the odd integers up to and including 2m^p-1;..." - p. 16.
%D C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Oxford University Press, 1966, pp. 16-17.
%H Winston de Greef, <a href="/A062207/b062207.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) = A013499(n) - 1 for n>=2. - _R. J. Mathar_, May 18 2007
%F E.g.f.: 2/(1 + LambertW(-x)) - exp(x). - _Vaclav Kotesovec_, Dec 21 2014
%e a(2)=7 and 1+3+5+7=16, which is A062206(2).
%e a(3)=53 and 1+3+5+...+53=729, which is A062206(3).
%t Table[2n^n-1,{n,20}] (* _Harvey P. Dale_, Jul 19 2015 *)
%o (PARI) { for (n=1, 100, write("b062207.txt", n, " ", 2*(n^n) - 1) ) } \\ _Harry J. Smith_, Aug 02 2009
%Y Cf. A013499, A062206.
%K easy,nonn
%O 0,3
%A _Jason Earls_, Jun 13 2001
%E More terms from Larry Reeves (larryr(AT)acm.org), Jun 15 2001
%E Definition simplified by _M. F. Hasler_, Sep 02 2012
%E a(0)=1 prepended by _Alois P. Heinz_, Feb 20 2023
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