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

0,9

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

Table of n, a(n) for n=0..70.

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.

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 *)

Prog

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

Crossrefs

Cf. A111246.

Sequence in context: A091925 A369199 A034370 * A264429 A324163 A127537

Adjacent sequences: A144399 A144400 A144401 * A144403 A144404 A144405

Keyword

nonn,tabl

Author

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

Status

approved