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A046860
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Triangle giving a(n,k) = number of k-colored labeled graphs with n nodes.
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1
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1, 1, 4, 1, 24, 48, 1, 160, 1152, 1536, 1, 1440, 30720, 122880, 122880, 1, 18304, 1152000, 10813440, 29491200, 23592960, 1, 330624, 65630208, 1348730880, 7707033600, 15854469120, 10569646080, 1, 8488960, 5858721792, 261070258176
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| R. C. Read, The number of k-colored graphs on labeled nodes, Canad. J. Math., 12 (1960), 410-414.
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FORMULA
| a(n, k) = Sum_{r=1..n-1} C(n, r) 2^(r*(n-r)) a(r, k-1).
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EXAMPLE
| 1; 1 4; 1 24 48;...
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MATHEMATICA
| a[n_ /; n >= 1, k_ /; k >= 1] := a[n, k] = Sum[ Binomial[n, r]*2^(r*(n - r))*a[r, k - 1], {r, 1, n - 1}]; a[_, 0] = 1; Flatten[ Table[ a[n, k], {n, 1, 8}, {k, 0, n - 1}]] (* From Jean-François Alcover, Dec 12 2011, after formula *)
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CROSSREFS
| Column #1 gives A000683.
Cf. A000683, A006201, A006202.
Sequence in context: A183875 A136232 A079621 * A089505 A062328 A136234
Adjacent sequences: A046857 A046858 A046859 * A046861 A046862 A046863
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KEYWORD
| tabl,easy,nice,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 04 2000
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