cp's OEIS Frontend

A084357 Number of sets of sets of lists.

%I A084357 #36 Jul 11 2020 07:53:59
%S A084357 1,1,4,23,171,1552,16583,203443,2813660,43258011,731183365,
%T A084357 13466814110,268270250977,5744515120489,131525839441428,
%U A084357 3205279987587275,82812074976214547,2260364854328771548,64979726427408468055,1961976154991285214707,62065551492895731512852
%N A084357 Number of sets of sets of lists.
%C A084357 In the book by Flajolet and Sedgewick on page 139 incorrectly gives a(5) = 1542. - _Vaclav Kotesovec_, Jul 11 2020
%D A084357 T. S. Motzkin, Sorting numbers ...: for a link to an annotated scanned version of this paper see A000262.
%D A084357 T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176.
%H A084357 T. D. Noe, <a href="/A084357/b084357.txt">Table of n, a(n) for n = 0..100</a>
%H A084357 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/books.html">Analytic Combinatorics</a>, 2009; see page 139.
%H A084357 K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, <a href="http://arXiv.org/abs/quant-ph/0312202">Hierarchical Dobinski-type relations via substitution and the moment problem</a> [J. Phys. A 37 (2004), 3475-3487]
%H A084357 K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, <a href="http://arXiv.org/abs/quant-ph/0312202">Hierarchical Dobinski-type relations via substitution and the moment problem</a>
%H A084357 N. J. A. Sloane and Thomas Wieder, <a href="http://arXiv.org/abs/math.CO/0307064">The Number of Hierarchical Orderings</a>, Order 21 (2004), 83-89.
%F A084357 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
%p A084357 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)];
%t A084357 a[n_] = Sum[ n!/k!*Binomial[n-1, k-1]*BellB[k], {k, 0, n}]; a[0] = 1; Array[a, 20, 0]
%t A084357 (* _Jean-François Alcover_, Jun 22 2011, after _Vladeta Jovovic_ *)
%Y A084357 Row sums of A079005 and row sums of A088814.
%Y A084357 Cf. A000110, A008297, A271703.
%K A084357 nonn
%O A084357 0,3
%A A084357 _N. J. A. Sloane_, Jun 22 2003