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A144402 Triangle in A144385 read downwards by columns.

%I A144402 #23 Mar 28 2020 06:37:13
%S A144402 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,
%T A144402 175,315,140,21,1,0,0,0,280,1225,980,266,28,1,0,0,0,280,3780,5565,
%U A144402 2520,462,36,1,0,0,0,0,9100,26145,19425,5670,750,45,1,0,0,0,0,15400
%N A144402 Triangle in A144385 read downwards by columns.
%C A144402 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
%H A144402 Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, <a href="http://arxiv.org/abs/1701.08394">Analysis of the Gift Exchange Problem</a>, arXiv:1701.08394 [math.CO], 2017.
%H A144402 David Applegate and N. J. A. Sloane, <a href="http://arxiv.org/abs/0907.0513">The Gift Exchange Problem</a>, arXiv:0907.0513 [math.CO], 2009.
%t A144402 BellMatrix[f_Function, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len-1}, {k, 0, len-1}]];
%t A144402 rows = 12;
%t A144402 M = BellMatrix[If[#<3, 1, 0]&, rows];
%t A144402 Table[M[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jul 14 2018, after _Peter Luschny_ *)
%o A144402 (Sage) # uses[bell_matrix from A264428]
%o A144402 bell_matrix(lambda n: 1 if n<3 else 0, 12) # _Peter Luschny_, Jan 19 2016
%Y A144402 Cf. A111246.
%K A144402 nonn,tabl
%O A144402 0,9
%A A144402 _David Applegate_ and _N. J. A. Sloane_, Dec 07 2008