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A264434
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Triangle read by rows, inverse Bell transform of the third-order Bell numbers, T(n,k) for n >= 0 and 0 <= k <= n.
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0
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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, 1, 0, -7, -56, 301, -350, 140, -21, 1, 0, 33, 35, -938, 1701, -1050, 266, -28, 1, 0, -102, 423, 2485, -7686, 6951, -2646, 462, -36, 1, 0, 240, -3219, -3450, 31885
(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, -1, 7, -6, 1]
[ 0, 1, -15, 25, -10, 1]
[ 0, 0, 31, -90, 65, -15, 1]
[ 0, -7, -56, 301, -350, 140, -21, 1]
[ 0, 33, 35, -938, 1701, -1050, 266, -28, 1]
[ 0, -102, 423, 2485, -7686, 6951, -2646, 462, -36, 1]
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PROG
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(Sage) # uses[bell_transform from A264428, inverse_bell_transform from A264429]
uno = [1]*dim
bell_numbers = [sum(bell_transform(n, uno)) for n in range(dim)]
bell_number_2 = [sum(bell_transform(n, bell_numbers)) for n in range(dim)]
bell_number_3 = [sum(bell_transform(n, bell_number_2)) for n in range(dim)]
return inverse_bell_transform(dim, bell_number_3)
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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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