A079639 Matrix product of Stirling1-triangle A008275(n,k) and unsigned Lah-triangle |A008297(n,k)|.

1, 1, 1, 2, 3, 1, 4, 11, 6, 1, 14, 40, 35, 10, 1, 38, 184, 195, 85, 15, 1, 216, 840, 1204, 665, 175, 21, 1, 600, 4920, 7616, 5369, 1820, 322, 28, 1, 6240, 26616, 54116, 44016, 18669, 4284, 546, 36, 1, 9552, 197856, 392460, 383480, 191205, 54453, 9030, 870, 45, 1, 319296, 1177176, 3229776, 3449600, 2017070, 679371, 139293, 17490, 1320, 55, 1, -519312

Offset: 1

Author

Vladeta Jovovic, Jan 30 2003

Keywords

• sign
• tabl

Comments

Also the Bell transform of A006252(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 26 2016

Crossrefs

Cf. A006252 (first column).

Programs

Maple

# The function BellMatrix is defined in A264428.
# Adds (1, 0, 0, 0, ..) as column 0.
BellMatrix(n -> add(k!*combinat:-stirling1(n+1,k),k=0..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}]];
rows = 12;
B = BellMatrix[Function[n, Sum[k!*StirlingS1[n+1, k], {k, 0, n+1}]], rows];
Table[B[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* Jean-François Alcover, Jun 27 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