This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A029706 #20 Apr 27 2013 02:17:33
%S A029706 2,10,46,226,1214,7106,44958,305090,2206398,16913986,136823262,
%T A029706 1163490498,10366252030,96491364674,935976996126,9440144423874,
%U A029706 98800604237118,1071092025420866,12008090971866206,139014305916844738
%N A029706 Sum C(n,k)*b(k), k=1..n, where b(k) is given by A001861.
%H A029706 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 A029706 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 A029706 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 A029706 (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 A029706 (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 A029706 Arises if one of the two kinds of boxes mentioned in A001861 may 'fail'.
%K A029706 nonn
%O A029706 0,1
%A A029706 Andre Poenitz (andre.poenitz(AT)mathematik.tu-chemnitz.de)
%E A029706 Added missing digit in the last term from _Jean-François Alcover_, Apr 26 2013