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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 22 2003
STATUS
approved