%I #20 Apr 27 2013 02:17:33

%S 2,10,46,226,1214,7106,44958,305090,2206398,16913986,136823262,

%T 1163490498,10366252030,96491364674,935976996126,9440144423874,

%U 98800604237118,1071092025420866,12008090971866206,139014305916844738

%N Sum C(n,k)*b(k), k=1..n, where b(k) is given by A001861.

%H Jacques Carlier and Corinne Lucet, <a href="http://dx.doi.org/10.1016/0166-218X(95)00032-M">A decomposition algorithm for network reliability evaluation</a>. In First International Colloquium on Graphs and Optimization (GOI), 1992 (Grimentz). Discrete Appl. Math. 65 (1996), 141-156 (see page 153 and Fig 6).

%F E.g.f.: 1/2 - exp(x) + 1/2*exp(2*exp(x)-2). a(n-2) = A035009(n)-1. - _Ralf Stephan_, Jan 26 2004

%t a[n_] := Sum[Binomial[n, k]*BellB[k, 2], {k, 1, n}]; Table[a[n], {n, 1, 20}] (* _Jean-François Alcover_, Apr 26 2013 *)

%o (PARI) x='x+O('x^66); Vec(serlaplace(1/2-exp(x)+1/2*exp(2*exp(x)-2))) \\ _Joerg Arndt_, Apr 21 2013

%o (PARI) a(n) = sum(k=1, n, binomial(n, k)*sum(j=1, k, stirling(k, j, 2)*2^j)); \\ \\ _Michel Marcus_, Apr 26 2013

%Y Arises if one of the two kinds of boxes mentioned in A001861 may 'fail'.

%K nonn

%O 0,1

%A Andre Poenitz (andre.poenitz(AT)mathematik.tu-chemnitz.de)

%E Added missing digit in the last term from _Jean-François Alcover_, Apr 26 2013