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A133709
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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).
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6
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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
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OFFSET
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1,3
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LINKS
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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.
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FORMULA
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Burger and van Vuuren give an explicit formula.
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EXAMPLE
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Triangle begins:
1
1 3 3
1 7 35 140 420 840 840
1 12 131 1435 15225 150570 1351770
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MAPLE
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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
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CROSSREFS
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Columns are given by A055998, A133710-A133712.
Sequence in context: A118408 A079268 A102316 * A173651 A124040 A160332
Adjacent sequences: A133706 A133707 A133708 * A133710 A133711 A133712
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KEYWORD
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nonn,tabf
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AUTHOR
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N. J. A. Sloane, Dec 30 2007
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STATUS
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approved
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