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A256041
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Triangle read by rows: number of idempotent basis elements of rank k in Brauer monoid B_n.
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0
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1, 0, 1, 0, 0, 1, 0, 6, 0, 1, 0, 0, 24, 0, 1, 0, 120, 0, 60, 0, 1, 0, 0, 1080, 0, 120, 0, 1, 0, 5040, 0, 5040, 0, 210, 0, 1, 0, 0, 80640, 0, 16800, 0, 336, 0, 1, 0, 362880, 0, 604800, 0, 45360, 0, 504, 0, 1, 0, 0, 9072000, 0, 3024000, 0, 105840, 0, 720, 0, 1
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OFFSET
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0,8
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COMMENTS
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LINKS
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EXAMPLE
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Triangle begins:
1,
0, 1,
0, 0, 1,
0, 6, 0, 1,
0, 0, 24, 0, 1,
0, 120, 0, 60, 0, 1,
0, 0, 1080, 0, 120, 0, 1,
0, 5040, 0, 5040, 0, 210, 0, 1,
0, 0, 80640, 0, 16800, 0, 336, 0, 1,
0, 362880, 0, 604800, 0, 45360, 0, 504, 0, 1,
0, 0, 9072000, 0, 3024000, 0, 105840, 0, 720, 0, 1,
...
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MAPLE
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# The function BellMatrix is defined in A264428.
BellMatrix(n -> `if`(n::odd, 0, (n+1)!), 9); # Peter Luschny, Jan 29 2016
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MATHEMATICA
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BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
B = BellMatrix[Function[n, If[OddQ[n], 0, (n + 1)!]], rows = 12];
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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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