OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..325
E. R. Canfield, Meet and join in the partition lattice, Electronic Journal of Combinatorics, 8 (2001) R15.
B. Pittel, Where the typical set partitions meet and join, Electronic Journal of Combinatorics, 7 (2000) R5.
Frank Simon, Algebraic Methods for Computing the Reliability of Networks, Dissertation, Doctor Rerum Naturalium (Dr. rer. nat.), Fakultät Mathematik und Naturwissenschaften der Technischen Universität Dresden, 2012. See Table 3.3. - N. J. A. Sloane, Jan 04 2013
FORMULA
EXAMPLE
For n = 2 there are exactly the following two pairs ({{1,2}},{{1},{2}}), ({{1},{2}},{{1,2}}) satisfying the imposed conditions.
MAPLE
with(combinat):
m:= proc(n) option remember; add(stirling1(n, k)*bell(k)^2, k=0..n) end:
a:= proc(n) option remember;
m(n) -add(binomial(n-1, k)*m(k)*a(n-k), k=1..n-1)
end:
seq(a(n), n=0..20); # Alois P. Heinz, Apr 20 2012
MATHEMATICA
m[n_] := m[n] = Sum[StirlingS1[n, k]*BellB[k]^2, {k, 0, n}]; a[n_] := a[n] = m[n] - Sum[ Binomial[n-1, k]*m[k]*a[n-k], {k, 1, n-1}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jul 15 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alexander Steinhardt (asteinh1(AT)hs-mittweida.de), Jens Schreiter (jschrei1(AT)hs-mittweida.de), Frank Simon, Apr 03 2012
EXTENSIONS
Terms corrected and more terms added, Alois P. Heinz, Apr 20 2012
STATUS
approved