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A125178
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Triangle read by rows: T(n,0)=B(n) (the Bell numbers, A000110(n)), T(n,k)=0 for k < 0 or k > n, T(n,k) = T(n-1,k) + T(n-1,k-1) for n >= 1, 0 <= k <= n.
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1
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1, 1, 1, 2, 2, 1, 5, 4, 3, 1, 15, 9, 7, 4, 1, 52, 24, 16, 11, 5, 1, 203, 76, 40, 27, 16, 6, 1, 877, 279, 116, 67, 43, 22, 7, 1, 4140, 1156, 395, 183, 110, 65, 29, 8, 1, 21147, 5296, 1551, 578, 293, 175, 94, 37, 9, 1, 115975, 26443, 6847, 2129, 871, 468, 269, 131, 46, 10, 1
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OFFSET
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0,4
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COMMENTS
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Row sums = 1, 2, 5, 13, 36, 109, 369, ...
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LINKS
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EXAMPLE
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First few rows of the triangle:
1;
1, 1;
2, 2, 1;
5, 4, 3, 1;
15, 9, 7, 4, 1;
52, 24, 16, 11, 5, 1;
203, 76, 40, 27, 16, 6, 1;
...
(4,3) = 16 = 7 + 9 = (3,3) + (3,2).
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MAPLE
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with(combinat): T:=proc(n, k) if k=0 then bell(n) elif k<0 or k>n then 0 else T(n-1, k)+T(n-1, k-1) fi end: for n from 0 to 11 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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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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