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A132311
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Triangle read by rows: T(n,k) = 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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3
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| T(n,k) = T(n,n-k);
T(n,0) = 1 for n>0;
A000041(n) - 1 <= T(n,1) <= A000041(n) for n>1;
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LINKS
| Index entries for triangles and arrays related to Pascal's triangle
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EXAMPLE
| 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.
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CROSSREFS
| Cf. A132312, A007318, A126257, A014631.
Sequence in context: A133135 A191687 A177254 * A199802 A121697 A124976
Adjacent sequences: A132308 A132309 A132310 * A132312 A132313 A132314
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KEYWORD
| nonn,tabl
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 18 2007
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