Search: id:A007778
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%I A007778
%S A007778 0,1,8,81,1024,15625,279936,5764801,134217728,3486784401,
%T A007778 100000000000,3138428376721,106993205379072,3937376385699289,
%U A007778 155568095557812224,6568408355712890625,295147905179352825856
%N A007778 n^(n+1).
%C A007778 Number of edges of the complete bipartite graph of order n+n^n, K_n,n^n 
               - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002
%C A007778 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
%C A007778 a(n) is also the number of ways of writing an n-cycle as the product 
               of n+1 transpositions. [From Nikos Apostolakis (nikos.ap(AT)gmail.com), 
               Nov 22 2008]
%D A007778 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 
               67.
%H A007778 N. Hobson, <a href="http://www.qbyte.org/puzzles/p048s.html">Exponential 
               equation</a>.
%F A007778 E.g.f.: -W(-x)/(1+W(-x))^3, W(x) Lambert's function (principal branch).
%p A007778 a:=n->mul(n, k=0..n): seq(a(n), n=0..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 26 2008
%p A007778 restart:a:=n->mul(sum(1, j=1..n), k=0..n): seq(a(n), n=0..16);# [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 01 2009]
%p A007778 with(finance):seq(futurevalue(1,n-2,n), n=1..17);# [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
%t A007778 lst={};Do[a=n^(n+1);AppendTo[lst, a], {n, 0, 2*4!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Oct 01 2008]
%Y A007778 Cf. A000169, A000272, A000312, A007830, A008785-A008791. Essentially 
               the same as A065440.
%Y A007778 Sequence in context: A098308 A055996 A068617 this_sequence A065440 A092366 
               A022519
%Y A007778 Adjacent sequences: A007775 A007776 A007777 this_sequence A007779 A007780 
               A007781
%K A007778 nonn,easy
%O A007778 0,3
%A A007778 N. J. A. Sloane (njas(AT)research.att.com).

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