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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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8
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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; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 18, Table 1.5.1.
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FORMULA
| 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
| 1; 1,2; 1,12,8; 1,80,192,64; ...
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MAPLE
| 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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MATHEMATICA
| maxn = 8; t[_, 1] = 1; t[n_, k_] := t[n, k] = Sum[ Binomial[n, j]*2^(j*(n - j))*t[j, k - 1]/k, {j, 1, n - 1}]; Flatten[ Table[t[n, k], {n, 1, maxn}, {k, 1, n}]] (* From Jean-François Alcover, Sep 21 2011 *)
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CROSSREFS
| 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 * A130559 A135256 A090586
Adjacent sequences: A058840 A058841 A058842 * A058844 A058845 A058846
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 07 2001
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