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A001866
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Number of connected graphs with n nodes and n edges.
(Formerly M5170 N2245)
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2
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0, 0, 1, 24, 936, 56640, 4968000, 598328640, 94916183040, 19200422062080, 4826695329792000, 1476585999504000000, 540272647694971699200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Or number of nXn (0,1) matrices with two 1's in each row the permanent of which equals to 2. Note that, if (0,1) matrix with two 1's in each row has positive permanent, the it equals to a power of 2. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Mar 25 2010]
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REFERENCES
| Austin, T. L.; Fagen, R. E.; Penney, W. F.; Riordan, John; The number of components in random linear graphs. Ann. Math. Statist 30 1959 747-754.
V. S. Shevelev, On the permanent of the stochastic (0,1)-matrices with equal row sums, Izvestia Vuzov of the North-Caucasus region, Nature sciences 1 (1997), 21-38 (in Russian). [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Mar 25 2010]
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| Explicit formula: a(n)=(n!^2*n^(n-1)/2)*Sum{k=2,...,n}n^(-k)/(n-k)!; Recursion: a(2)=1, for n>=3, a(n)=n!*((n-1)!/2+Sum{k=2,...,n-1}(-1)^(n+k+1)*k^(n-k)*C(n,k)a(k)/k! [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Mar 25 2010]
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CROSSREFS
| A174586 [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Mar 25 2010]
Sequence in context: A061236 A001784 A172206 * A033590 A174586 A189048
Adjacent sequences: A001863 A001864 A001865 * A001867 A001868 A001869
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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