|
| |
|
|
A084357
|
|
Number of sets of sets of lists.
|
|
4
| |
|
|
1, 1, 4, 23, 171, 1552, 16583, 203443, 2813660, 43258011, 731183365, 13466814110, 268270250977, 5744515120489, 131525839441428, 3205279987587275, 82812074976214547, 2260364854328771548, 64979726427408468055, 1961976154991285214707
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
REFERENCES
| T. S. Motzkin, Sorting numbers ...: for a link to this paper see A000262.
T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
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 37 (2004), 3475-3487]
K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, Hierarchical Dobinski-type relations via substitution and the moment problem
N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 139
|
|
|
FORMULA
| E.g.f.: exp(exp(x/(1-x))-1). Lah transform of Bell numbers: Sum_{k=0..n} n!/k!*binomial(n-1, k-1)*Bell(k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 28 2003
|
|
|
MAPLE
| with(combstruct); SetSetSeqL := [T, {T=Set(S), S=Set(U, card >= 1), U=Sequence(Z, card >=1)}, labeled]; [seq(count(%, size=j), j=1..12)];
|
|
|
MATHEMATICA
| a[n_] = Sum[ n!/k!*Binomial[n-1, k-1]*BellB[k], {k, 0, n}]; a[0] = 1; Array[a, 20, 0]
(* From Jean-François Alcover, Jun 22 2011, after V. Jovovic *)
|
|
|
CROSSREFS
| Row sums of A079005 and row sums of A088814.
Sequence in context: A158884 A053525 A113869 * A075729 A127131 A083355
Adjacent sequences: A084354 A084355 A084356 * A084358 A084359 A084360
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 22 2003
|
| |
|
|
