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 A189898 Triangular array read by rows.  T(n,k) is the number of digraphs with n labeled nodes having exactly k undirected (or weak) components, n >= 1, 1 <= k <= n. 2
 1, 3, 1, 54, 9, 1, 3834, 243, 18, 1, 1027080, 20790, 675, 30, 1, 1067308488, 6364170, 67635, 1485, 45, 1, 4390480193904, 7543111716, 23031540, 171045, 2835, 63, 1, 72022346388181584, 35217115838604, 30469951764, 63580545, 370440, 4914, 84, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Bell transform of A003027(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 18 2016 LINKS Alois P. Heinz, Rows n = 1..32, flattened FORMULA E.g.f. for column k: log(A(x))^k/k! where A(x) is the e.g.f. for A053763. EXAMPLE 1 3       1 54      9     1 3834    243   18   1 1027080 20790 675  30  1 MAPLE T:= (n, k)-> coeff(series(log(add(2^(i^2-i) *x^i/i!, i=0..n))^k /k!,                    x, n+1), x, n) *n!: seq(seq(T(n, k), k=1..n), n=1..10);  # Alois P. Heinz, May 01 2011 MATHEMATICA a= Sum[4^Binomial[n, 2]x^n/n!, {n, 0, 10}]; Transpose[Map[Drop[#, 1] &, Table[Range[0, 10]! CoefficientList[Series[Log[a]^n/n!, {x, 0, 10}], x], {n, 1, 10}]]] // Grid PROG (Sage) # uses[bell_matrix from A264428, A003027] # Adds a column 1, 0, 0, 0, ... at the left side of the triangle. bell_matrix(lambda n: A003027(n+1), 10) # Peter Luschny, Jan 18 2016 CROSSREFS Column 1 = A003027, row sums = A053763, lower diagonal = A045943. Sequence in context: A322730 A292425 A095988 * A082525 A162221 A213127 Adjacent sequences:  A189895 A189896 A189897 * A189899 A189900 A189901 KEYWORD nonn,tabl,changed AUTHOR Geoffrey Critzer, May 01 2011 EXTENSIONS Name clarified by Andrew Howroyd, Jan 11 2022 STATUS approved

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Last modified January 20 21:46 EST 2022. Contains 350472 sequences. (Running on oeis4.)