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A003084
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Related to number of digraphs.
(Formerly M3993)
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2
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1, 5, 40, 801, 46821, 9185102, 6163297995, 14339791643249, 117235455142196308, 3412474003994007703605, 357748249084029269153547905, 136400554886800212073525651823742
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 124, table 5.1.2, p*a_p
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| Sum a(n) x^n / n = log (1 + Sum d(n) x^n ), where d(n) is # digraphs on n nodes (A000273 ).
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MATHEMATICA
| Needs["Combinatorica`"]; d[n_] := GraphPolynomial[n, x, Directed] /. x -> 1; max = 12; se = Series[ Sum[ a[n]*x^n/n, {n, 1, max}] - Log[1 + Sum[ d[n]*x^n, {n, 1, max}]], {x, 0, max}]; sol = SolveAlways[ se == 0, x]; A003084 = Table[ a[n], {n, 1, max}] /. sol[[1]] (* From Jean-François Alcover, Feb 01 2012, after formula *)
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CROSSREFS
| Sequence in context: A113079 A138427 A005330 * A010573 A043083 A041599
Adjacent sequences: A003081 A003082 A003083 * A003085 A003086 A003087
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 09 2000
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