A133709 Triangle read by rows: T(m,l) = number of labeled covers of size l of a finite set of m unlabeled elements (m >= 1, 1 <= l <= 2^m - 1).

1, 1, 3, 3, 1, 7, 35, 140, 420, 840, 840, 1, 12, 131, 1435, 15225, 150570, 1351770, 10810800, 75675600, 454053600, 2270268000, 9081072000, 27243216000, 54486432000, 54486432000, 1, 18, 347, 7693, 185031, 4568046, 111793710, 2661422400

Offset

1,3

Links

Table of n, a(n) for n=1..34.

A. P. Burger and J. H. van Vuuren, Balanced minimal covers of a finite set, Discr. Math. 307 (2007), 2853-2860.

Formula

Burger and van Vuuren give an explicit formula.

Example

Triangle begins:
1
1 3 3
1 7 35 140 420 840 840
1 12 131 1435 15225 150570 1351770

Maple

A133709 := proc(m, l)
        option remember;
        if l = 1 then
                1;
        else
                add((-1)^i*binomial(l, i)*binomial(2^(l-i)+m-2, m), i=0..l-1)
                - add(combinat[stirling2](l, i)*procname(m, i), i=1..l-1) ;
        end if;
end proc:
seq(seq(A133709(m, l), l=1..2^m-1), m=1..5) ; # R. J. Mathar, Nov 23 2011

Mathematica

T[m_, l_] := T[m, l] = If[l == 1, 1, Sum[(-1)^i Binomial[l, i] Binomial[ 2^(l-i)+m-2, m], {i, 0, l-1}] - Sum[StirlingS2[l, i] T[m, i], {i, 1, l-1} ] ];
Table[T[m, l], {m, 1, 5}, {l, 1, 2^m-1}] // Flatten (* Jean-François Alcover, Apr 01 2020, from Maple *)

Crossrefs

Columns are given by A055998, A133710, A133711, A133712.

Sequence in context: A261767 A355315 A300620 * A173651 A330337 A124040

Adjacent sequences: A133706 A133707 A133708 * A133710 A133711 A133712

Keyword

nonn,tabf

Author

N. J. A. Sloane, Dec 30 2007

Status

approved