A084357 Number of sets of sets of lists.
1, 1, 4, 23, 171, 1552, 16583, 203443, 2813660, 43258011, 731183365, 13466814110, 268270250977, 5744515120489, 131525839441428, 3205279987587275, 82812074976214547, 2260364854328771548, 64979726427408468055, 1961976154991285214707, 62065551492895731512852
Offset: 0
Keywords
References
- T. S. Motzkin, Sorting numbers ...: for a link to an annotated scanned version of 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
- P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 139.
- 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.
Programs
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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] (* Jean-François Alcover, Jun 22 2011, after Vladeta Jovovic *)
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, Sep 28 2003
Comments