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%I #21 Mar 26 2020 15:53:43
%S 1,0,1,0,-1,1,0,1,-3,1,0,0,7,-6,1,0,-5,-10,25,-10,1,0,18,-20,-75,65,
%T -15,1,0,-7,231,70,-315,140,-21,1,0,-338,-840,1064,945,-980,266,-28,1,
%U 0,2215,-1278,-8918,1512,4935,-2520,462,-36,1
%N Triangle read by rows, inverse Bell transform of Bell numbers.
%H Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/BellTransform">The Bell transform</a>
%e [ 1 ]
%e [ 0, 1 ]
%e [ 0, -1, 1 ]
%e [ 0, 1, -3, 1 ]
%e [ 0, 0, 7, -6, 1 ]
%e [ 0, -5, -10, 25, -10, 1 ]
%e [ 0, 18, -20, -75, 65, -15, 1 ]
%e [ 0, -7, 231, 70, -315, 140, -21, 1 ]
%e [ 0, -338, -840, 1064, 945, -980, 266, -28, 1 ]
%e [ 0, 2215, -1278, -8918, 1512, 4935, -2520, 462, -36, 1 ]
%t rows = 10;
%t M = Table[BellY[n, k, BellB[Range[0, rows-1]]],{n, 0, rows-1}, {k, 0, rows-1}] // Inverse;
%t A264429 = Table[M[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jun 22 2018 *)
%o (Sage) # uses[bell_transform from A264428]
%o def inverse_bell_transform(dim, L):
%o M = matrix(ZZ, dim)
%o for n in range(dim):
%o row = bell_transform(n, L)
%o for k in (0..n): M[n,k] = row[k]
%o return M.inverse()
%o def A264429_matrix(dim):
%o uno = [1]*dim
%o bell_numbers = [sum(bell_transform(n, uno)) for n in range(dim)]
%o return inverse_bell_transform(dim, bell_numbers)
%o A264429_matrix(10)
%Y Cf. A000110, A264428.
%K sign,tabl
%O 0,9
%A _Peter Luschny_, Nov 13 2015
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