A029706 Sum C(n,k)*b(k), k=1..n, where b(k) is given by A001861.

2, 10, 46, 226, 1214, 7106, 44958, 305090, 2206398, 16913986, 136823262, 1163490498, 10366252030, 96491364674, 935976996126, 9440144423874, 98800604237118, 1071092025420866, 12008090971866206, 139014305916844738

Offset: 0

Author

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

Keywords

• nonn

Links

• Jacques Carlier and Corinne Lucet, A decomposition algorithm for network reliability evaluation. In First International Colloquium on Graphs and Optimization (GOI), 1992 (Grimentz). Discrete Appl. Math. 65 (1996), 141-156 (see page 153 and Fig 6).

Crossrefs

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

Programs

Mathematica

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

PARI

x='x+O('x^66); Vec(serlaplace(1/2-exp(x)+1/2*exp(2*exp(x)-2))) \\ Joerg Arndt, Apr 21 2013

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

Formula

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

Extensions

Added missing digit in the last term from Jean-François Alcover, Apr 26 2013