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A132311
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Triangle read by rows: T(n,k) is the number of partitions of binomial(n,k) into parts of the first n rows of Pascal's triangle, 0<=k<=n.
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4
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0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 4, 7, 4, 1, 1, 6, 28, 28, 6, 1, 1, 11, 117, 318, 117, 11, 1, 1, 14, 388, 3344, 3344, 388, 14, 1, 1, 21, 1757, 71277, 290521, 71277, 1757, 21, 1, 1, 29, 8270, 2031198, 53679222, 53679222, 2031198, 8270, 29, 1, 1, 42, 40243, 74464383, 19465193506, 147286801214, 19465193506, 74464383, 40243, 42, 1
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OFFSET
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0,8
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COMMENTS
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T(n,k) = T(n,n-k).
T(n,0) = 1 for n>0.
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LINKS
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EXAMPLE
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A007318(4,2) = A007318(6,1) = 6: T(4,2) = #{3+3, 3+2+1, 3+1+1+1, 2+2+2, 2+2+1+1, 2+1+1+1+1, 1+1+1+1+1+1} = 7, but T(6,1) = A000041(6) = 11.
Triangle T(n,k) begins:
0;
1, 1;
1, 1, 1;
1, 2, 2, 1;
1, 4, 7, 4, 1;
1, 6, 28, 28, 6, 1;
1, 11, 117, 318, 117, 11, 1;
1, 14, 388, 3344, 3344, 388, 14, 1;
1, 21, 1757, 71277, 290521, 71277, 1757, 21, 1;
...
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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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