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, 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

Offset: 1

Author

Geoffrey Critzer, Nov 27 2014

Keywords

• nonn
• tabl

Comments

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

Examples

			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;
		

Crossrefs

Column 1 = A001929.

Row sums = A000798.

Programs

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 *)

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

Formula

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