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 A062207 2*n^n-1. 4
 1, 7, 53, 511, 6249, 93311, 1647085, 33554431, 774840977, 19999999999, 570623341221, 17832200896511, 605750213184505, 22224013651116031, 875787780761718749, 36893488147419103231, 1654480523772673528353 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 Harry J. Smith, Table of n, a(n) for n=1,...,100 FORMULA a(n) = A013499(n) - 1. - 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. A062206. Sequence in context: A057180 A137612 A092802 * A194929 A317689 A116202 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 STATUS approved

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Last modified May 15 02:21 EDT 2021. Contains 343909 sequences. (Running on oeis4.)