OFFSET
0,3
REFERENCES
J. de la Cal, J. Carcamo, Set partitions and moments of random variables, J. Math. Anal. Applic. 378 (2011) 16 doi:10.1016/j.jmaa.2011.01.002 Remark 5
J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.4.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..440
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
Jekuthiel Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353. [Annotated scanned copy]
Gottfried Helms, Bell Numbers, 2008.
T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346.
T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346. (Annotated scanned copy)
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 293
K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, Hierarchical Dobinski-type relations via substitution and the moment problem, arXiv:quant-ph/0312202, 2003.
K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, Hierarchical Dobinski-type relations via substitution and the moment problem, J. Phys. A: Math.Gen 37 (2004) 3475-3487.
John Riordan, Letter, Apr 28 1976.
Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565 [math.CO], 2010.
FORMULA
E.g.f.: exp(exp(exp(exp(x)-1)-1)-1).
a(n) = sum(sum(sum(stirling2(n,k) *stirling2(k,m) *stirling2(m,r), k=m..n), m=r..n), r=1..n), n>0. - Vladimir Kruchinin, Sep 08 2010
MAPLE
g:= proc(p) local b; b:= proc(n) option remember; `if`(n=0, 1, (n-1)! *add(p(k)*b(n-k)/ (k-1)!/ (n-k)!, k=1..n)) end end: a:= g(g(g(1))): seq(a(n), n=0..30); # Alois P. Heinz, Sep 11 2008
MATHEMATICA
nn = 18; a = Exp[Exp[x] - 1]; b = Exp[a - 1];
Range[0, nn]! CoefficientList[Series[Exp[b - 1], {x, 0, nn}], x] (*Geoffrey Critzer, Dec 28 2011*)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Extended with new definition by Christian G. Bower, Aug 15 1998
STATUS
approved