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A322279
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Array read by antidiagonals: T(n,k) is the number of connected graphs on n labeled nodes, each node being colored with one of k colors, where no edge connects two nodes of the same color.
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8
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1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 2, 0, 0, 1, 4, 6, 6, 0, 0, 1, 5, 12, 42, 38, 0, 0, 1, 6, 20, 132, 618, 390, 0, 0, 1, 7, 30, 300, 3156, 15990, 6062, 0, 0, 1, 8, 42, 570, 9980, 136980, 668526, 134526, 0, 0, 1, 9, 56, 966, 24330, 616260, 10015092, 43558242, 4172198, 0, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,8
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COMMENTS
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Not all colors need to be used.
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LINKS
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FORMULA
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k-th column is the logarithmic transform of the k-th column of A322280.
E.g.f of k-th column: 1 + log(Sum_{n>=0} A322280(n,k)*x^n/n!).
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EXAMPLE
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Array begins:
===============================================================
n\k| 0 1 2 3 4 5 6
---+-----------------------------------------------------------
0 | 1 1 1 1 1 1 1 ...
1 | 0 1 2 3 4 5 6 ...
2 | 0 0 2 6 12 20 30 ...
3 | 0 0 6 42 132 300 570 ...
4 | 0 0 38 618 3156 9980 24330 ...
5 | 0 0 390 15990 136980 616260 1956810 ...
6 | 0 0 6062 668526 10015092 65814020 277164210 ...
7 | 0 0 134526 43558242 1199364852 11878194300 67774951650 ...
...
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PROG
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(PARI)
M(n)={
my(p=sum(j=0, n, x^j/(j!*2^binomial(j, 2))) + O(x*x^n));
my(q=sum(j=0, n, x^j*2^binomial(j, 2)) + O(x*x^n));
my(W=Mat(vector(n, k, Col(serlaplace(1 + log(serconvol(q, p^k)))))));
matconcat([1, W]);
}
my(T=M(7)); for(n=1, #T, print(T[n, ]))
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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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