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A049055
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Triangle read by rows, giving T(n,k) = number of k-member minimal ordered covers of a labeled n-set (1 <= k <= n).
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2
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1, 1, 2, 1, 12, 6, 1, 50, 132, 24, 1, 180, 1830, 1560, 120, 1, 602, 20460, 60960, 20520, 720, 1, 1932, 201726, 1856400, 2047920, 302400, 5040, 1, 6050, 1832292, 48550824, 155801520, 72586080, 4979520, 40320, 1, 18660, 15717750, 1144994760, 10006131240, 13069123200, 2767474080, 91082880, 362880
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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Triangle starts
1;
1, 2;
1, 12, 6;
1, 50, 132, 24;
...
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MATHEMATICA
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t[n_, k_] := Sum[ (-1)^i*Binomial[k, i]*(2^k - 1 - i)^n, {i, 0, k}]; Flatten[ Join[{1}, Table[t[n, k], {n, 1, 9}, {k, 1, n}]]] (* Jean-François Alcover, Dec 12 2011, after Michael Somos *)
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PROG
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(PARI) {T(n, k)=sum(i=0, k, (-1)^i*binomial(k, i)*(2^k-1-i)^n)} /* Michael Somos, Oct 16 2006 */
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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