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A007778 n^(n+1). 41
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

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 A092366 A022519 A138439

Adjacent sequences:  A007775 A007776 A007777 * A007779 A007780 A007781

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 8 15:08 EST 2016. Contains 278945 sequences.