A079642 Matrix product of unsigned Stirling1-triangle |A008275(n,k)| and Stirling1-triangle A008275(n,k).

1, 0, 1, 1, 0, 1, 1, 4, 0, 1, 8, 5, 10, 0, 1, 26, 58, 15, 20, 0, 1, 194, 217, 238, 35, 35, 0, 1, 1142, 2035, 1008, 728, 70, 56, 0, 1, 9736, 13470, 11611, 3444, 1848, 126, 84, 0, 1, 81384, 134164, 85410, 47815, 9660, 4116, 210, 120, 0, 1, 823392, 1243770, 983059

Offset: 1

Author

Vladeta Jovovic, Jan 30 2003

Keywords

• nonn
• tabl

Comments

Also the Bell transform of A089064(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 26 2016

Examples

			1; 0,1; 1,0,1; 1,4,0,1; 8,5,10,0,1; 26,58,15,20,0,1; ...
		

Programs

Maple

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

Mathematica

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, Sum[(-1)^n*(k-1)! StirlingS1[n+1, k], {k, 1, n+1} ] ], rows = 12];
Table[B[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* Jean-François Alcover, Jun 28 2018, after Peter Luschny *)

Formula

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

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