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A055154
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Triangle read by rows: T(n,k) = number of k-covers of a labeled n-set, k=1..2^n-1.
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9
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1, 1, 3, 1, 1, 12, 32, 35, 21, 7, 1, 1, 39, 321, 1225, 2919, 4977, 6431, 6435, 5005, 3003, 1365, 455, 105, 15, 1, 1, 120, 2560, 24990, 155106, 711326, 2597410, 7856550, 20135050, 44337150, 84665490, 141118250, 206252550, 265182450, 300540190
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row sums give A003465.
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 165.
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FORMULA
| T(n, k)=Sum_{j=0..n} (-1)^j*C(n, j)*C(2^(n-j)-1, k), k=1..2^n-1.
Also T(n, k) = (1/k!)*Sum_{j=0..k} Stirling1(k+1, j+1)*(2^j-1)^n. E.g.f.: Sum(exp(y*(2^n-1))*ln(1+x)^n/n!, n=0..infinity)/(1+x). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 30 2004
Also exp(-y)*Sum((1+x)^(2^n-1)*y^n/n!, n=0..infinity).
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EXAMPLE
| [1],[1,3,1],[1,12,32,35,21,7,1],...; There are 35 4-covers of a labeled 3-set.
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CROSSREFS
| Cf. A054780, A055621.
Columns: A029858, A095152-A095155.
Sequence in context: A156584 A129619 A094573 * A015112 A174690 A156869
Adjacent sequences: A055151 A055152 A055153 * A055155 A055156 A055157
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KEYWORD
| easy,nonn,tabf
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 14 2000
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