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A213597
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Triangle T(n,k), n>=1, 0<=k<=A000041(n), read by rows: row n gives the coefficients of the chromatic polynomial of the ranked poset L(n) of partitions of n, highest powers first.
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2
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1, 0, 1, -1, 0, 1, -2, 1, 0, 1, -5, 10, -9, 3, 0, 1, -9, 36, -79, 98, -64, 17, 0, 1, -17, 136, -666, 2192, -5032, 8111, -9013, 6569, -2818, 537, 0, 1, -28, 378, -3242, 19648, -88676, 306308, -819933, 1703404, -2723374, 3285552, -2887734, 1739326, -639065, 107435, 0
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OFFSET
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1,7
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COMMENTS
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The ranked poset L(n) of partitions is defined in A002846. A partition of n into k parts is connected to another partition of n into k+1 parts that results from splitting one part of the first partition into two parts.
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LINKS
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EXAMPLE
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L(5): (32)---(221)
/ \ / \
/ X \
/ / \ \
(5)---(41)---(311)---(2111)---(11111)
Chromatic polynomial: q^7-9*q^6+36*q^5-79*q^4+98*q^3-64*q^2+17*q.
Triangle T(n,k) begins:
1, 0;
1, -1, 0;
1, -2, 1, 0;
1, -5, 10, -9, 3, 0;
1, -9, 36, -79, 98, -64, 17, 0;
1, -17, 136, -666, 2192, -5032, 8111, -9013, 6569, -2818, 537, 0;
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CROSSREFS
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Row sums (for n>1) and last elements of rows give: A000004.
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KEYWORD
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sign,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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