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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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3
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0, 0, 1, 24, 936, 56640, 4968000, 598328640, 94916183040, 19200422062080, 4826695329792000, 1476585999504000000, 540272647694971699200, 233019960215154829516800, 117009251702203840384204800, 67680314823703303654732800000, 44677678066673631080900198400000
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OFFSET
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0,4
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COMMENTS
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Or number of n X n (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, then it is equal to a power of 2. [Vladimir Shevelev, Mar 25 2010]
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REFERENCES
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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). [Vladimir Shevelev, 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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LINKS
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FORMULA
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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! [Vladimir Shevelev, Mar 25 2010]
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MATHEMATICA
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Join[{0}, Table[(n!^2*n^(n - 1)/2)*Sum[n^(-k)/(n - k)!, {k, 2, n}], {n, 20}]] (* T. D. Noe, Aug 10 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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