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

0,1

Links

Table of n, a(n) for n=0..19.

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).

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A137193 A006213 A137635 * A191644 A009640 A191684

Adjacent sequences: A029703 A029704 A029705 * A029707 A029708 A029709

Keyword

nonn

Author

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

Extensions

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

Status

approved