A144402 Triangle in A144385 read downwards by columns.

1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 0, 7, 6, 1, 0, 0, 10, 25, 10, 1, 0, 0, 10, 75, 65, 15, 1, 0, 0, 0, 175, 315, 140, 21, 1, 0, 0, 0, 280, 1225, 980, 266, 28, 1, 0, 0, 0, 280, 3780, 5565, 2520, 462, 36, 1, 0, 0, 0, 0, 9100, 26145, 19425, 5670, 750, 45, 1, 0, 0, 0, 0, 15400

Offset: 0

Author

David Applegate and N. J. A. Sloane, Dec 07 2008

Keywords

• nonn
• tabl

Comments

The Bell transform of the sequence "g(n) = 1 if n<3 else 0". For the definition of the Bell transform see A264428. - Peter Luschny, Jan 19 2016

Links

• Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, Analysis of the Gift Exchange Problem, arXiv:1701.08394 [math.CO], 2017.
• David Applegate and N. J. A. Sloane, The Gift Exchange Problem, arXiv:0907.0513 [math.CO], 2009.

Crossrefs

Cf. A111246.

Programs

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[If[#<3, 1, 0]&, rows];
Table[M[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jul 14 2018, after Peter Luschny *)

Sage

# uses[bell_matrix from A264428]
bell_matrix(lambda n: 1 if n<3 else 0, 12) # Peter Luschny, Jan 19 2016