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Search: id:A058843
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| A058843 |
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Triangle T(n,k) = C_n(k) where C_n(k) = number of k-colored labeled graphs with n nodes (n >= 1, 1<=k<=n). |
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9
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| 1, 1, 2, 1, 12, 8, 1, 80, 192, 64, 1, 720, 5120, 5120, 1024, 1, 9152, 192000, 450560, 245760, 32768, 1, 165312, 10938368, 56197120, 64225280, 22020096, 2097152, 1, 4244480, 976453632, 10877927424, 23781703680, 15971909632, 3758096384
(list; table; graph; listen)
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OFFSET
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1,3
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REFERENCES
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F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 18, Table 1.5.1.
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FORMULA
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C_n(k) = Sum_{i=1..n-1} binomial(n, i)*2^(i*(n-i))*C_i(k-1)/k.
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EXAMPLE
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1; 1,2; 1,12,8; 1,80,192,64; ...
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MAPLE
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for p from 1 to 20 do C[p, 1] := 1; od: for k from 2 to 20 do for p from 1 to k-1 do C[p, k] := 0; od: od: for k from 2 to 10 do for p from k to 10 do C[p, k] := add( binomial(p, n)*2^(n*(p-n))*C[n, k-1]/k, n=1..p-1); od: od:
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CROSSREFS
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Apart from scaling, same as A058875. Columns give A058872 and A000683, A058873 and A006201, A058874 and A006202, also A006218.
Sequence in context: A085752 A074966 A128413 this_sequence A130559 A135256 A090586
Adjacent sequences: A058840 A058841 A058842 this_sequence A058844 A058845 A058846
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 07 2001
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