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A189898 Triangular array read by rows.  T(n,k) is the number of weakly connected digraphs with n nodes having exactly k components. n >= 1, 1 <= k <= n. 1
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)

# The function bell_matrix is defined in A264428.

# 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

AUTHOR

Geoffrey Critzer, May 01 2011

STATUS

approved

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Last modified November 19 06:03 EST 2019. Contains 329310 sequences. (Running on oeis4.)