0,3

Also number of distinct resistances possible for n arbitrary resistors each connected in series or parallel with previous ones (cf. A051045).

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..

Stanley's Problem 5.4(a) involves threshold graphs; Problem 5.4(c) involves hyperplane arrangements.

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]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.4(a).

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]

T. D. Noe, Table of n, a(n) for n=0..100

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

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, ...

2*A053525(n), n>1.

Adjacent sequences: A005837 A005838 A005839 this_sequence A005841 A005842 A005843

Sequence in context: A006664 A141117 A145844 this_sequence A161881 A088791 A111552

nonn,easy,nice

Simon Plouffe (simon.plouffe(AT)gmail.com)