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A228534 Triangular array read by rows: T(n,k) is the number of functional digraphs on {1,2,...,n} such that every element is mapped to a recurrent element and there are exactly k cycles, n>=1, 1<=k<=n. 1
1, 3, 1, 11, 9, 1, 58, 71, 18, 1, 409, 620, 245, 30, 1, 3606, 6274, 3255, 625, 45, 1, 38149, 73339, 45724, 11795, 1330, 63, 1, 470856, 977780, 697004, 221529, 33880, 2506, 84, 1, 6641793, 14678712, 11602394, 4309956, 823179, 82908, 4326, 108, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Bell transform of (-1)^n*A009444(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 18 2016

LINKS

Alois P. Heinz, Rows n = 1..90, flattened

FORMULA

E.g.f.: 1/(1 - x*exp(x))^y.

EXAMPLE

       1;

       3,      1;

      11,      9,      1;

      58,     71,     18,      1;

     409,    620,    245,     30,     1;

    3606,   6274,   3255,    625,    45,    1;

   38149,  73339,  45724,  11795,  1330,   63,  1;

  470856, 977780, 697004, 221529, 33880, 2506, 84, 1;

MAPLE

# The function BellMatrix is defined in A264428.

# Adds (1, 0, 0, 0, ..) as column 0.

g := n -> add(m^(n-m)*m!*binomial(n+1, m), m=1..n+1);

BellMatrix(g, 9); # Peter Luschny, Jan 29 2016

MATHEMATICA

nn = 8; a = x Exp[x];

Map[Select[#, # > 0 &] &,

  Drop[Range[0, nn]! CoefficientList[

     Series[1/(1 - a)^y, {x, 0, nn}], {x, y}], 1]] // Grid

(* Second program: *)

BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];

B = BellMatrix[Function[n, (n+1)! Sum[m^(n-m)/(n-m+1)!, {m, 1, n+1}]], rows = 12];

Table[B[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* Jean-Fran├žois Alcover, Jun 28 2018, after Peter Luschny *)

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: (-1)^n*A009444(n+1), 10) # Peter Luschny, Jan 18 2016

CROSSREFS

Row sums = A006153.

Column 1 = |A009444|.

Cf. A199673.

Sequence in context: A135574 A008969 A199577 * A119908 A153257 A002185

Adjacent sequences:  A228531 A228532 A228533 * A228535 A228536 A228537

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Aug 24 2013

STATUS

approved

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Last modified October 18 01:01 EDT 2018. Contains 316297 sequences. (Running on oeis4.)