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a(n) = 2*n^n-1.
4

%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