The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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