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A272582 The number of strongly connected digraphs with n vertices and n+1 edges.

%I A272582 #39 Jan 15 2022 12:30:04
%S A272582 0,9,84,720,6480,63000,665280,7620480,94348800,1257379200,17962560000,
%T A272582 273988915200,4446092851200,76498950528000,1391365527552000,
%U A272582 26676557107200000,537799391281152000,11373816888225792000,251805357846282240000,5824367407574876160000
%N A272582 The number of strongly connected digraphs with n vertices and n+1 edges.
%C A272582 Wright also gives the number of strongly connected digraphs with n vertices and n+2 edges, 0, 6, 316, 6440, 107850, 1719060, 27476400, ... (offset 2) in terms of a polynomial of order 5 multiplied by n!. - _R. J. Mathar_, May 12 2016
%H A272582 Andrew Howroyd, <a href="/A272582/b272582.txt">Table of n, a(n) for n = 2..200</a>
%H A272582 E. M. Wright, <a href="http://dx.doi.org/10.1093/qmath/28.3.363">Formulae for the number of sparsely-edged strong labelled digraphs</a>, Quart. J. Math. 28 (3) (1977) 363-367, Section 3.
%F A272582 a(n) = (n-2)*(n+3)*n!/4.
%F A272582 E.g.f.: x^3*(3 - 2*x)/(2*(1 - x)^3). - _Ilya Gutkovskiy_, May 10 2016
%F A272582 D-finite with recurrence -(n+1)*(n-4)*a(n) +(n-1)*(n-3)*(n+2)*a(n-1)=0. - _R. J. Mathar_, Mar 11 2021
%t A272582 Table[(n-2)(n+3)n!/4,{n,2,30}] (* _Harvey P. Dale_, May 23 2017 *)
%o A272582 (Python)
%o A272582 from __future__ import print_function
%o A272582 from sympy import factorial
%o A272582 for n in range(2,500):
%o A272582    print((int)((n-2)*(n+3)*factorial(n)/4),end=", ")
%o A272582 # _Soumil Mandal_, May 12 2016
%o A272582 (PARI) a(n) = (n-2)*(n+3)*n!/4 \\ _Andrew Howroyd_, Jan 15 2022
%Y A272582 A diagonal of A057273.
%K A272582 nonn,easy
%O A272582 2,2
%A A272582 _R. J. Mathar_, May 10 2016