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A247232 Triangular array read by rows: T(n,k) is the number of pre-orders on an n-set with exactly k connected components in its digraph representation, n>=1, 1<=k<=n. 1
1, 3, 1, 19, 9, 1, 233, 103, 18, 1, 4851, 1735, 325, 30, 1, 158175, 43201, 7320, 785, 45, 1, 7724333, 1567783, 218491, 22960, 1610, 63, 1, 550898367, 82142943, 8856974, 818461, 59570, 2954, 84, 1, 56536880923, 6187176225, 496368181, 37205658, 2518131, 135198, 4998, 108, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Bell transform of A001929(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 18 2016

LINKS

Table of n, a(n) for n=1..45.

FORMULA

E.g.f.: A(exp(x)-1)^y where A(x) is the e.g.f. for A001035.

EXAMPLE

1;

3, 1;

19, 9, 1;

233, 103, 18, 1;

4851, 1735, 325, 30, 1;

158175, 43201, 7320, 785, 45, 1;

7724333, 1567783, 218491, 22960, 1610, 63, 1;

550898367, 82142943, 8856974, 818461, 59570, 2954, 84, 1;

MATHEMATICA

A001035 = Cases[Import["https://oeis.org/A001035/b001035.txt", "Table"], {_, _}][[All, 2]];

lg = Length[A001035];

A[x_] = Sum[A001035[[n + 1]] x^n/n!, {n, 0, lg - 1}];

Rest[CoefficientList[#, y]]& /@ (CoefficientList[A[Exp[x] - 1]^y + O[x]^lg, x]*Range[0, lg - 1]!) // Flatten (* Jean-François Alcover, Jan 01 2020 *)

PROG

(Sage) # uses[bell_matrix from A264428]

# Adds a column 1, 0, 0, 0, ... at the left side of the triangle.

topo = oeis('A001929') # Fetch the data via Internet.

A001929List = topo.first_terms()

A001929 = lambda n: A001929List[n]

bell_matrix(lambda n: A001929(n+1), 10) # Peter Luschny, Jan 18 2016, updated Mar 25 2020

CROSSREFS

Column 1 = A001929.

Row sums = A000798.

Sequence in context: A086156 A227888 A188109 * A147076 A027537 A192721

Adjacent sequences: A247229 A247230 A247231 * A247233 A247234 A247235

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Nov 27 2014

STATUS

approved

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Last modified February 2 23:07 EST 2023. Contains 360024 sequences. (Running on oeis4.)