%I A004123 M1975
%S A004123 1,2,10,74,730,9002,133210,2299754,45375130,1007179562,24840104410,
%T A004123 673895590634,19944372341530,639455369290922,22079273878443610,
%U A004123 816812844197444714,32232133532123179930,1351401783010933015082
%N A004123 Number of generalized weak orders on n points.
%C A004123 Number of bipartitional relations on a set of cardinality n. - Ralf Stephan, 
               Apr 27 2003
%D A004123 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A004123 Wagner, Carl G.; Enumeration of generalized weak orders. Arch. Math. 
               (Basel) 39 (1982), no. 2, 147-152.
%H A004123 T. D. Noe, <a href="b004123.txt">Table of n, a(n) for n=1..100</a>
%H A004123 P. Blasiak, K. A. Penson and A. I. Solomon, <a href="http://arXiv.org/
               abs/quant-ph/0303030">Dobinski-type relations and the log-normal 
               distribution</a>.
%H A004123 C. G. Bower, <a href="transforms2.html">Transforms</a>
%H A004123 Foata, D. and Krattenthaler, C., <a href="http://citeseer.ist.psu.edu/
               foata95graphical.html">Graphical Major Indices, II</a>, Seminaire 
               Lotharingien de Combinatoire, B34k, 16 pp., 1995.
%H A004123 D. Foata and D. Zeilberger, <a href="http://arXiv.org/abs/math.CO/9406220">
               [math/9406220] The Graphical Major Index</a>
%F A004123 a(n) = sum(k^n*(2/3)^k, k = 0..infinity)/3; a(n) = sum(stirling2(n, k)*(2^k)*k!, 
               k = 0..n); E.g.f. : 1/(3-2*exp(x))
%F A004123 Stirling transform of A000165. - Karol A. Penson (penson(AT)lptl.jussieu.fr), 
               Jan 25 2002
%F A004123 "AIJ" (ordered, indistinct, labeled) transform of 2, 2, 2, 2...
%F A004123 Recurrence: a(n) = 2*Sum_{k=1..n} binomial(n, k)*a(n-k), a(0)=1. - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Mar 27 2003
%F A004123 E.g.f.: 1/(3 - 2e^x).
%Y A004123 Cf. A004121, A004122, A000165, A000670, A032033.
%Y A004123 Second row of array A094416 (generalized ordered Bell numbers).
%Y A004123 Equals 2 * A050351(n) for n>0.
%Y A004123 Sequence in context: A046863 A000698 A092881 this_sequence A086352 A005365 
               A059104
%Y A004123 Adjacent sequences: A004120 A004121 A004122 this_sequence A004124 A004125 
               A004126
%K A004123 nonn,nice,easy
%O A004123 1,2
%A A004123 N. J. A. Sloane (njas(AT)research.att.com).
%E A004123 More terms from Christian G. Bower (bowerc(AT)usa.net)