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A062207
a(n) = 2*n^n-1.
4
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
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
Sequence in context: A057180 A137612 A092802 * A073564 A372939 A194929
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