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A264429
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Triangle read by rows, inverse Bell transform of Bell numbers.
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9
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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, -15, 1, 0, -7, 231, 70, -315, 140, -21, 1, 0, -338, -840, 1064, 945, -980, 266, -28, 1, 0, 2215, -1278, -8918, 1512, 4935, -2520, 462, -36, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,9
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LINKS
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EXAMPLE
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[ 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, -15, 1 ]
[ 0, -7, 231, 70, -315, 140, -21, 1 ]
[ 0, -338, -840, 1064, 945, -980, 266, -28, 1 ]
[ 0, 2215, -1278, -8918, 1512, 4935, -2520, 462, -36, 1 ]
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MATHEMATICA
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rows = 10;
M = Table[BellY[n, k, BellB[Range[0, rows-1]]], {n, 0, rows-1}, {k, 0, rows-1}] // Inverse;
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PROG
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(Sage) # uses[bell_transform from A264428]
def inverse_bell_transform(dim, L):
M = matrix(ZZ, dim)
for n in range(dim):
row = bell_transform(n, L)
for k in (0..n): M[n, k] = row[k]
return M.inverse()
uno = [1]*dim
bell_numbers = [sum(bell_transform(n, uno)) for n in range(dim)]
return inverse_bell_transform(dim, bell_numbers)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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