A079640 Matrix product of unsigned Stirling1-triangle |A008275(n,k)| and unsigned Lah-triangle |A008297(n,k)|.

1, 3, 1, 14, 9, 1, 88, 83, 18, 1, 694, 860, 275, 30, 1, 6578, 10084, 4245, 685, 45, 1, 72792, 132888, 69244, 14735, 1435, 63, 1, 920904, 1950024, 1209880, 318969, 41020, 2674, 84, 1, 13109088, 31580472, 22715972, 7133784, 1137549, 98028, 4578, 108, 1

Offset: 1

Author

Vladeta Jovovic, Jan 30 2003

Keywords

• nonn
• tabl

Comments

Also the Bell transform of A007840(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 26 2016

Examples

			1; 3,1; 14,9,1; 88,83,18,1; 694,860,275,30,1; 6578,10084,4245,685,45,1; ...
		

Crossrefs

Cf. A007840 (first column).

Programs

Maple

# The function BellMatrix is defined in A264428.
# Adds (1, 0, 0, 0, ..) as column 0.
BellMatrix(n -> add(k!*abs(combinat:-stirling1(n+1, k)), k=0..n+1), 9); # Peter Luschny, Jan 26 2016

Mathematica

BellMatrix[f_Function, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
rows = 12;
M = BellMatrix[Function[n, Sum[k!*Abs[StirlingS1[n+1, k]], {k, 0, n+1}]], rows];
Table[M[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* Jean-François Alcover, Jun 26 2018, after Peter Luschny *)

Formula

T(n, k) = Sum_{i=k..n} |A008275(n, i)| * |A008297(i, k)|.

E.g.f.: (1-x)^(-y/(1+log(1-x))). - Vladeta Jovovic, Nov 22 2003