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A151512
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The triangle in A151359 read by rows upwards.
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1
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1, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 6, 7, 1, 0, 1, 10, 25, 15, 1, 0, 1, 15, 65, 90, 31, 1, 0, 1, 21, 140, 350, 301, 63, 0, 0, 1, 28, 266, 1050, 1701, 966, 119, 0, 0, 1, 36, 462, 2646, 6951, 7770, 2989, 210, 0, 0, 1, 45, 750, 5880, 22827, 42525, 33985, 8925, 336, 0, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,8
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COMMENTS
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Conjectured: The i-th element of row j is the number of different equivalence relationships, within a set of (j-1) element, having (j-i) equivalence classes. For example: row 5 = [1, 6, 7, 1, 0] means that, in a set of 4 elements, there exists 7 equivalence relationships having 3 different equivalence classes. - Philippe Beaudoin, Nov 09 2013
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LINKS
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EXAMPLE
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Triangle begins:
1
1 0
1 1 0
1 3 1 0
1 6 7 1 0
1 10 25 15 1 0
1 15 65 90 31 1 0
1 21 140 350 301 63 0 0
1 28 266 1050 1701 966 119 0 0
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MATHEMATICA
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Unprotect[Power]; 0^0 = 1; a[n_ /; 1 <= n <= 6] = 1; a[_] = 0; t[n_, k_] := t[n, k] = If[k == 0, a[0]^n, Sum[Binomial[n - 1, j - 1] a[j] t[n - j, k - 1], {j, 0, n - k + 1}]]; Table[Table[t[n - 1, k], {k, n - 1, 0, -1}], {n, 0, 10}] // Flatten (* Jean-François Alcover, Jan 20 2016, using Peter Luschny's Bell transform *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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