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

%I #39 Jan 15 2022 12:30:04

%S 0,9,84,720,6480,63000,665280,7620480,94348800,1257379200,17962560000,

%T 273988915200,4446092851200,76498950528000,1391365527552000,

%U 26676557107200000,537799391281152000,11373816888225792000,251805357846282240000,5824367407574876160000

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

%C 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 Andrew Howroyd, <a href="/A272582/b272582.txt">Table of n, a(n) for n = 2..200</a>

%H 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 a(n) = (n-2)*(n+3)*n!/4.

%F E.g.f.: x^3*(3 - 2*x)/(2*(1 - x)^3). - _Ilya Gutkovskiy_, May 10 2016

%F 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 Table[(n-2)(n+3)n!/4,{n,2,30}] (* _Harvey P. Dale_, May 23 2017 *)

%o (Python)

%o from __future__ import print_function

%o from sympy import factorial

%o for n in range(2,500):

%o print((int)((n-2)*(n+3)*factorial(n)/4),end=", ")

%o # _Soumil Mandal_, May 12 2016

%o (PARI) a(n) = (n-2)*(n+3)*n!/4 \\ _Andrew Howroyd_, Jan 15 2022

%Y A diagonal of A057273.

%K nonn,easy

%O 2,2

%A _R. J. Mathar_, May 10 2016

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)