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%I #15 Mar 26 2020 15:55:18
%S 1,0,1,0,1,1,0,3,3,1,0,14,15,6,1,0,89,100,45,10,1,0,716,834,405,105,
%T 15,1,0,6967,8351,4284,1225,210,21,1,0,79524,97596,52220,16009,3080,
%U 378,28,1,0,1041541,1303956,721674,233268,48699,6804,630,36,1
%N Triangle read by rows, inverse Bell transform of the complementary Bell numbers (A000587); T(n,k) for n>=0 and 0<=k<=n.
%H Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/BellTransform">The Bell transform</a>
%F Row sums are A029768(n-1) for n>=1.
%F T(n,1) = A007549(n) for n>=1.
%e Triangle starts:
%e 1,
%e 0, 1,
%e 0, 1, 1,
%e 0, 3, 3, 1,
%e 0, 14, 15, 6, 1,
%e 0, 89, 100, 45, 10, 1,
%e 0, 716, 834, 405, 105, 15, 1,
%e 0, 6967, 8351, 4284, 1225, 210, 21, 1,
%e 0, 79524, 97596, 52220, 16009, 3080, 378, 28, 1
%o (Sage) # uses[bell_transform from A264428, inverse_bell_transform from A264429]
%o def A264436_matrix(dim):
%o uno = [1]*dim
%o complementary_bell_numbers = [sum((-1)^n*b for (n, b) in enumerate (bell_transform(n, uno))) for n in (0..dim)]
%o return inverse_bell_transform(dim, complementary_bell_numbers)
%o A264436_matrix(9)
%Y Cf. A000587, A007549, A029768, A264428, A264429.
%K nonn,tabl
%O 0,8
%A _Peter Luschny_, Dec 01 2015
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