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A191249 Triangular array T(n,k) read by rows:  number of labeled relations of the n-set with exactly k connected components. 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..28.

FORMULA

E.g.f. for column k: log(A(x))^k/k! where A(x) is the E.g.f. for A002416

EXAMPLE

2

12       4

432      72     8

61344    3888   288   16

32866560 665280 21600 960 32

MATHEMATICA

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

CROSSREFS

Sequence in context: A159323 A038218 A264841 * A005760 A155892 A286480

Adjacent sequences:  A191246 A191247 A191248 * A191250 A191251 A191252

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, May 28 2011

STATUS

approved

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Last modified February 25 12:01 EST 2020. Contains 332233 sequences. (Running on oeis4.)