A062207 a(n) = 2*n^n-1.

1, 1, 7, 53, 511, 6249, 93311, 1647085, 33554431, 774840977, 19999999999, 570623341221, 17832200896511, 605750213184505, 22224013651116031, 875787780761718749, 36893488147419103231, 1654480523772673528353, 78692816150593075150847, 3956839311320627178247957

Offset: 0

Author

Jason Earls, Jun 13 2001

Keywords

• easy
• nonn

Comments

Also: a(n) = 2m-1 where m is given by Sum_{i = 1..m } 2*i-1 = n^(2*n) (A062206).

"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.

Examples

			a(2)=7 and 1+3+5+7=16, which is A062206(2).
a(3)=53 and 1+3+5+...+53=729, which is A062206(3).
		

References

• C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Oxford University Press, 1966, pp. 16-17.

Links

• Winston de Greef, Table of n, a(n) for n = 0..385

Crossrefs

Cf. A013499, A062206.

Programs

Mathematica

Table[2n^n-1,{n,20}] (* Harvey P. Dale, Jul 19 2015 *)

PARI

{ for (n=1, 100, write("b062207.txt", n, " ", 2*(n^n) - 1) ) } \\ Harry J. Smith, Aug 02 2009

Formula

a(n) = A013499(n) - 1 for n>=2. - R. J. Mathar, May 18 2007

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

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 15 2001

Definition simplified by M. F. Hasler, Sep 02 2012

a(0)=1 prepended by Alois P. Heinz, Feb 20 2023