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

0,3

Comments

In the book by Flajolet and Sedgewick on page 139 incorrectly gives a(5) = 1542. - Vaclav Kotesovec, Jul 11 2020

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.

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

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 *)

Crossrefs

Row sums of A079005 and row sums of A088814.

Cf. A000110, A008297, A271703.

Sequence in context: A208676 A317276 A113869 * A360868 A075729 A328006

Adjacent sequences: A084354 A084355 A084356 * A084358 A084359 A084360

Keyword

nonn

Author

N. J. A. Sloane, Jun 22 2003

Status

approved