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%I #22 Jan 30 2021 02:12:46
%S 1,0,1,0,-1,1,0,1,-3,1,0,-1,7,-6,1,0,1,-15,25,-10,1,0,0,31,-90,65,-15,
%T 1,0,-7,-56,301,-350,140,-21,1,0,33,35,-938,1701,-1050,266,-28,1,0,
%U -102,423,2485,-7686,6951,-2646,462,-36,1,0,240,-3219,-3450,31885
%N Triangle read by rows, inverse Bell transform of the third-order Bell numbers, T(n,k) for n >= 0 and 0 <= k <= n.
%e [ 1]
%e [ 0, 1]
%e [ 0, -1, 1]
%e [ 0, 1, -3, 1]
%e [ 0, -1, 7, -6, 1]
%e [ 0, 1, -15, 25, -10, 1]
%e [ 0, 0, 31, -90, 65, -15, 1]
%e [ 0, -7, -56, 301, -350, 140, -21, 1]
%e [ 0, 33, 35, -938, 1701, -1050, 266, -28, 1]
%e [ 0, -102, 423, 2485, -7686, 6951, -2646, 462, -36, 1]
%o (Sage) # uses[bell_transform from A264428, inverse_bell_transform from A264429]
%o def A264434_matrix(dim):
%o uno = [1]*dim
%o bell_numbers = [sum(bell_transform(n, uno)) for n in range(dim)]
%o bell_number_2 = [sum(bell_transform(n, bell_numbers)) for n in range(dim)]
%o bell_number_3 = [sum(bell_transform(n, bell_number_2)) for n in range(dim)]
%o return inverse_bell_transform(dim, bell_number_3)
%o A264434_matrix(10)
%Y Cf. A048993, A264428, A264429, A264431.
%K sign,tabl
%O 0,9
%A _Peter Luschny_, Dec 02 2015
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