%I A144331
%S A144331 1,0,1,1,0,0,1,3,3,0,0,0,1,6,15,15,0,0,0,0,1,10,45,105,105,0,0,0,0,
%T A144331 0,1,15,105,420,945,945,0,0,0,0,0,0,1,21,210,1260,4725,10395,10395,
%U A144331 0,0,0,0,0,0,0,1,28,378,3150,17325,62370,135135,135135,0,0,0,0,0,0
%N A144331 Triangle b(n,k) read by rows (n >= 0, 0 <= k <= 2n). See A144299 for 
               definition and properties.
%C A144331 Although this entry is the last of the versions of the underlying triangle 
               to be added to the OEIS, for some applications it is the most important.
%C A144331 Row n has 2n+1 entries.
%C A144331 A001498 has a b-file.
%H A144331 David Applegate and N. J. A. Sloane, <a href="http://arxiv.org/abs/0907.0513">
               The Gift Exchange Problem</a> (arXiv:0907.0513, 2009)
%F A144331 E.g.f.: Sum_{n >= 0} Sum_{k = 0..2n} b(n,k) y^n x^k/k! = exp(y(x+x^2/
               2)).
%F A144331 b(n,k) = n!/(2^(n-k)*(2*n-k)!*(k-n)!).
%e A144331 Triangle begins:
%e A144331 [1]
%e A144331 [0, 1, 1]
%e A144331 [0, 0, 1, 3, 3]
%e A144331 [0, 0, 0, 1, 6, 15, 15]
%e A144331 [0, 0, 0, 0, 1, 10, 45, 105, 105]
%e A144331 [0, 0, 0, 0, 0, 1, 15, 105, 420, 945, 945]
%e A144331 [0, 0, 0, 0, 0, 0, 1, 21, 210, 1260, 4725, 10395, 10395]
%e A144331 ...
%Y A144331 Cf. A144299. Row sums give A001515, column sums A000085.
%Y A144331 Other versions of this triangle are given in A001497, A001498, A111924 
               and A100861.
%Y A144331 See A144385 for a generalization.
%Y A144331 Sequence in context: A036113 A140351 A110492 this_sequence A167259 A000876 
               A109247
%Y A144331 Adjacent sequences: A144328 A144329 A144330 this_sequence A144332 A144333 
               A144334
%K A144331 nonn,tabf,nice
%O A144331 0,8
%A A144331 David Applegate and N. J. A. Sloane (njas(AT)research.att.com), Dec 07 
               2008