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URL: https://oeis.org/A001866

⇱ A001866 - OEIS

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A001866
Number of connected graphs with n nodes and n edges.
3
0, 0, 1, 24, 936, 56640, 4968000, 598328640, 94916183040, 19200422062080, 4826695329792000, 1476585999504000000, 540272647694971699200, 233019960215154829516800, 117009251702203840384204800, 67680314823703303654732800000, 44677678066673631080900198400000
OFFSET
0,4
COMMENTS
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
REFERENCES
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).
LINKS
T. L. Austin, R. E. Fagen, W. F. Penney, and John Riordan, The number of components in random linear graphs, Ann. Math. Statist 30 1959 747-754.
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)*binomial(n,k)*a(k)/k!). - Vladimir Shevelev, Mar 25 2010
a(n) ~ Pi * n^(2*n) / (2*exp(n)). - Vaclav Kotesovec, Nov 30 2017
MATHEMATICA
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 *)
CROSSREFS
Cf. A174586.
Sequence in context: A220804 A220253 A262583 * A033590 A174586 A254619
KEYWORD
nonn
STATUS
approved