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A257566
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Triangle read by rows, T(n,k) = Sum_{j=0..n-k+1} P(n,j)*T(n-j,k-1) if k>0 else 0^n where P(n,j) is the number of j-partitions of n; for n>=0 and 0<=k<=n.
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1
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1, 0, 1, 0, 2, 1, 0, 3, 4, 1, 0, 5, 13, 7, 1, 0, 7, 30, 30, 10, 1, 0, 11, 76, 119, 65, 14, 1, 0, 15, 152, 357, 306, 113, 18, 1, 0, 22, 330, 1119, 1375, 746, 193, 23, 1, 0, 30, 633, 2973, 5059, 3888, 1497, 295, 28, 1, 0, 42, 1245, 8036, 18605, 19423, 10298, 2930, 447, 34, 1
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OFFSET
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0,5
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LINKS
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FORMULA
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EXAMPLE
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1;
0, 1;
0, 2, 1;
0, 3, 4, 1;
0, 5, 13, 7, 1;
0, 7, 30, 30, 10, 1;
0, 11, 76, 119, 65, 14, 1;
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MAPLE
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T := proc(n, k) option remember; `if`(k=0, 0^n,
add(combinat:-numbpart(n, j)*T(n-j, k-1), j=0..n-k+1)) end:
for n from 0 to 12 do seq(T(n, k), k=0..n) od;
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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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