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

0,3

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.

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

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

Example

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).

Mathematica

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

Prog

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

Crossrefs

Cf. A013499, A062206.

Sequence in context: A057180 A137612 A092802 * A073564 A194929 A317689

Adjacent sequences: A062204 A062205 A062206 * A062208 A062209 A062210

Keyword

easy,nonn

Author

Jason Earls, Jun 13 2001

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

Status

approved