This site is supported by donations to The OEIS Foundation.

The October issue of the Notices of the Amer. Math. Soc. has an article about the OEIS.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A007778 a(n) = n^(n+1). 48
 0, 1, 8, 81, 1024, 15625, 279936, 5764801, 134217728, 3486784401, 100000000000, 3138428376721, 106993205379072, 3937376385699289, 155568095557812224, 6568408355712890625, 295147905179352825856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of edges of the complete bipartite graph of order n+n^n, K_n,n^n - Roberto E. Martinez II, Jan 07 2002 All rational solutions to the equation x^y = y^x, with x < y, are given by x = A000169(n+1)/A000312(n), y = A000312(n+1)/A007778(n), where n = 1, 2, 3, ... . - Nick Hobson Nov 30 2006 a(n) is also the number of ways of writing an n-cycle as the product of n+1 transpositions. [Nikos Apostolakis, Nov 22 2008] REFERENCES Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 67. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 N. Hobson, Exponential equation. Yidong Sun, Jujuan Zhuang, lambda-factorials of n, arXiv:1007.1339. [From Peter Luschny, Jul 09 2010] FORMULA E.g.f.: -W(-x)/(1+W(-x))^3, W(x) Lambert's function (principal branch). a(n) = Sum_{k=0..n} binomial(n,k)*A000166(k+1)*(n+1)^(n-k). [Peter Luschny, Jul 09 2010] See A008517 and A134991 for similar e.g.f.s. and A048993. - Tom Copeland, Oct 03 2011 E.g.f.: d/dx {x/(T(x)*(1-T(x))}, where T(x) = sum {n >= 1} n^(n-1)*x^n/n! is the tree function of A000169. - Peter Bala, Aug 05 2012 a(n) = n*A000312(n). - R. J. Mathar, Jan 12 2017 MATHEMATICA lst={}; Do[a=n^(n+1); AppendTo[lst, a], {n, 0, 2*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 01 2008 *) PROG (MAGMA)  [n^(n+1):n in [0..20]]; // Vincenzo Librandi, Jan 03 2012 (Maxima) A007778[n]:=n^(n+1)\$ makelist(A007778[n], n, 0, 30); /* Martin Ettl, Oct 29 2012 */ CROSSREFS Cf. A000169, A000272, A000312, A007830, A008785-A008791. Essentially the same as A065440. Cf. A061250, A143857. [From Reinhard Zumkeller, Jul 23 2010] Sequence in context: A207994 A210127 * A065440 A318047 A092366 A022519 Adjacent sequences:  A007775 A007776 A007777 * A007779 A007780 A007781 KEYWORD nonn,easy AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 24 07:30 EDT 2018. Contains 315308 sequences. (Running on oeis4.)