%I A005840 M1872
%S A005840 1,1,2,8,46,332,2874,29024,334982,4349492,62749906,995818760,17239953438,
%T A005840 323335939292,6530652186218,141326092842416,3262247252671414,80009274870905732,
%U A005840 2077721713464798210,56952857434896699992,1643312099715631960910
%N A005840 Expansion of (1-x)*e^x/(2-e^x).
%C A005840 Also number of distinct resistances possible for n arbitrary resistors 
               each connected in series or parallel with previous ones (cf. A051045).
%C A005840 The n-th term of A051045 uses the n different resistances 1, ..., n ohms, 
               whereas the problem corresponding to A005840 allows arbitrary general 
               resistances a1, a2, ..., an, chosen so as to give the maximum possible 
               number of distinct equivalent resistances - Eric Weisstein..
%C A005840 Stanley's Problem 5.4(a) involves threshold graphs; Problem 5.4(c) involves 
               hyperplane arrangements.
%C A005840 a(n) is the number of labeled threshold graphs on n vertices. [This is 
               more specific than the reference to Stanley.] [From Svante Janson 
               (svante.janson(AT)math.uu.se), Apr 01 2009]
%D A005840 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005840 R. P. Stanley, ``A zonotope associated with graphical degree sequences,
               '' in Applied Geometry and Discrete Combinatorics. DIMACS Series 
               in Discrete Math., Amer. Math. Soc., Vol. 4, pp. 555-570, 1991.
%D A005840 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Problem 5.4(a).
%D A005840 J.S. Beissinger and U.N. Peled, Enumeration of labelled threshold graphs 
               and a theorem of Frobenius involving Eulerian polynomials, J Graphs 
               Combin., 3 (1987), 213--219. MR903610 [From Svante Janson (svante.janson(AT)math.uu.se), 
               Apr 01 2009]
%H A005840 T. D. Noe, <a href="b005840.txt">Table of n, a(n) for n=0..100</a>
%H A005840 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ResistorNetwork.html">Link to a section of The World of Mathematics.</
               a>
%e A005840 exp(x)*(1-x)/(2-exp(x)) = 1 + x + x^2 + 4/3*x^3 + 23/12*x^4 + 83/30*x^5 
               + 479/120*x^6 + 1814/315*x^7 + O(x^8); then the coefficients are 
               multiplied by n! to get 1, 1, 2, 8, 46, 332, 2874, 29024, ...
%Y A005840 2*A053525(n), n>1.
%Y A005840 Sequence in context: A006664 A141117 A145844 this_sequence A161881 A088791 
               A111552
%Y A005840 Adjacent sequences: A005837 A005838 A005839 this_sequence A005841 A005842 
               A005843
%K A005840 nonn,easy,nice
%O A005840 0,3
%A A005840 Simon Plouffe (simon.plouffe(AT)gmail.com)