%I A069321
%S A069321 1,1,5,31,233,2071,21305,249271,3270713,47580151,760192505,13234467511,
%T A069321 249383390393,5057242311031,109820924003705,2542685745501751,
%U A069321 62527556173577273,1627581948113854711,44708026328035782905
%N A069321 Stirling transform of A001563 : a(0)=1, a(n)=sum(stirling2(n,k)*k*k!,
               k=1..n), n=1,2...
%C A069321 The number of compatible bipartitions of a set of cardinality n for which 
               at least one subset is not underlined. E.g. for n=2 there are 5 such 
               bipartitions: {1 2}, {1}{2}, {2}{1}, _{1}_{2}, _{2}_{1}. A005649 
               is the number of bipartitions of a set of cardinality n. A000670 
               is the number of bipartitions of a set of cardinality n with none 
               of the subsets underlined. - T. Kyle Petersen (tkpeters(AT)brandeis.edu), 
               Mar 31 2005
%D A069321 D. Foata and D. Zeilberger, "Graphical major indices," J. Comput. Appl. 
               Math. 68 (1996), no. 1-2, 79-101.
%H A069321 D. Foata and D. Zeilberger, <a href="http://front.math.ucdavis.edu/math.CO/
               9406220">The Graphical Major Index</a>.
%F A069321 Representation as an infinite series, in Maple notation : a(0)=1, a(n)= 
               sum(k^n*(k-1)/(2^k), k=2..infinity)/4, n=1, 2... This is a Dobinski-type 
               summation formula. E.g.f.: (exp(x)-1)/((2-exp(x))^2).
%F A069321 a(n)=(A000629(n+1)-A000629(n))/4 - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Oct 20 2002
%Y A069321 Cf. A001563.
%Y A069321 a(n) = (1/2)*(A000670(n+1)-A000670(n)).
%Y A069321 Cf. A005649, A000670.
%Y A069321 Sequence in context: A001910 A052773 A062147 this_sequence A082579 A024451 
               A046852
%Y A069321 Adjacent sequences: A069318 A069319 A069320 this_sequence A069322 A069323 
               A069324
%K A069321 nonn
%O A069321 0,3
%A A069321 Karol A. Penson (penson(AT)lptl.jussieu.fr), Mar 14 2002