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%I #23 Nov 26 2018 11:37:01
%S 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,
%T -666,2192,-5032,8111,-9013,6569,-2818,537,0,1,-28,378,-3242,19648,
%U -88676,306308,-819933,1703404,-2723374,3285552,-2887734,1739326,-639065,107435,0
%N 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.
%C 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.
%H Alois P. Heinz, <a href="/A213597/b213597.txt">Rows n = 1..9, flattened</a>
%H Olivier Gérard, <a href="/A002846/a002846.png">The ranked posets L(2),...,L(8)</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic Polynomial</a>
%e L(5): (32)---(221)
%e / \ / \
%e / X \
%e / / \ \
%e (5)---(41)---(311)---(2111)---(11111)
%e Chromatic polynomial: q^7-9*q^6+36*q^5-79*q^4+98*q^3-64*q^2+17*q.
%e Triangle T(n,k) begins:
%e 1, 0;
%e 1, -1, 0;
%e 1, -2, 1, 0;
%e 1, -5, 10, -9, 3, 0;
%e 1, -9, 36, -79, 98, -64, 17, 0;
%e 1, -17, 136, -666, 2192, -5032, 8111, -9013, 6569, -2818, 537, 0;
%Y Row lengths give: 1+A000041(n) = A052810(n).
%Y Row sums (for n>1) and last elements of rows give: A000004.
%Y Columns k=1-2 give: A000012, (-1)*A000097(n-2).
%Y Cf. A002846, A213242, A213385, A213427.
%K sign,tabf
%O 1,7
%A _Alois P. Heinz_, Jun 15 2012
%E Edited by _Alois P. Heinz_ at the suggestion of _Gus Wiseman_, May 02 2016
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