OFFSET
1,3
LINKS
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
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Dec 30 2007
STATUS
approved