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A191249
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Triangular array T(n,k) read by rows: number of labeled relations of the n-set with exactly k connected components.
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0
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2, 12, 4, 432, 72, 8, 61344, 3888, 288, 16, 32866560, 665280, 21600, 960, 32, 68307743232, 407306880, 4328640, 95040, 2880, 64, 561981464819712, 965518299648, 2948037120, 21893760, 362880, 8064, 128
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OFFSET
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1,1
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COMMENTS
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T(n,k) is the number of binary relations R on {1,2,...,n} such that the reflexive, symmetric and transitive closure of R is an equivalence relation with exactly k classes.
Row sums are A002416 = 2^(n^2).
Column 1 is A062738.
T(n,n) = 2^n is the number of binary relations that are a subset of the diagonal relation.
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LINKS
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Table of n, a(n) for n=1..28.
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FORMULA
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E.g.f. for column k: log(A(x))^k/k! where A(x) is the E.g.f. for A002416
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EXAMPLE
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2
12 4
432 72 8
61344 3888 288 16
32866560 665280 21600 960 32
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MATHEMATICA
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a=Sum[2^(n^2) x^n/n!, {n, 0, 10}];
Transpose[Table[Drop[Range[0, 10]! CoefficientList[Series[Log[a]^n/n!, {x, 0, 10}], x], 1], {n, 1, 10}]] // Grid
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CROSSREFS
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Sequence in context: A066700 A159323 A038218 * A005760 A155892 A112100
Adjacent sequences: A191246 A191247 A191248 * A191250 A191251 A191252
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KEYWORD
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nonn,tabl
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AUTHOR
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Geoffrey Critzer, May 28 2011
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STATUS
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approved
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