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A003027
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Number of weakly connected digraphs with n nodes.
(Formerly M3161)
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12
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1, 3, 54, 3834, 1027080, 1067308488, 4390480193904, 72022346388181584, 4721717643249254751360, 1237892809110149882059440768, 1298060596773261804821355107253504
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| R. W. Robinson, Counting labeled acyclic digraphs, pp. 239-273 of F. Harary, editor, New Directions in the Theory of Graphs. Academic Press, NY, 1973.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..30
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FORMULA
| a(n) = A062738(n)/2^n, since binary relations = digraphs with loops. - Ralf Stephan and Vladeta Jovovic, Mar 24 2004
E.g.f.: log(sum n>=0, 2^(n^2-n)*x^n/n!)
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MATHEMATICA
| Range[0, 20]! CoefficientList[Series[D[1 + Log[Sum[2^(n^2 - n) x^n/n!, {n, 0, 20}]], x], {x, 0, 20}], x]
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PROG
| (PARI) v=Vec(log(sum(n=0, default(seriesprecision), 2^(n^2-n)*x^n/n!))); for(i=1, #v, v[i]*=(i-1)!); v \\ Charles R Greathouse IV, Feb 14 2011
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CROSSREFS
| Sequence in context: A171213 A006025 A049414 * A054545 A158103 A174579
Adjacent sequences: A003024 A003025 A003026 * A003028 A003029 A003030
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KEYWORD
| nonn,easy,nice
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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, Goran Kilibarda (vladeta(AT)eunet.rs).
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