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

0, 9, 84, 720, 6480, 63000, 665280, 7620480, 94348800, 1257379200, 17962560000, 273988915200, 4446092851200, 76498950528000, 1391365527552000, 26676557107200000, 537799391281152000, 11373816888225792000, 251805357846282240000, 5824367407574876160000

Offset: 2

Author

R. J. Mathar, May 10 2016

Keywords

• nonn
• easy

Comments

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..200
• E. M. Wright, Formulae for the number of sparsely-edged strong labelled digraphs, Quart. J. Math. 28 (3) (1977) 363-367, Section 3.

Crossrefs

A diagonal of A057273.

Programs

Mathematica

Table[(n-2)(n+3)n!/4,{n,2,30}] (* Harvey P. Dale, May 23 2017 *)

PARI

a(n) = (n-2)*(n+3)*n!/4 \\ Andrew Howroyd, Jan 15 2022

Python

from _future_ import print_function
from sympy import factorial
for n in range(2,500):
   print((int)((n-2)*(n+3)*factorial(n)/4),end=", ")
# Soumil Mandal, May 12 2016

Formula

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

E.g.f.: x^3*(3 - 2*x)/(2*(1 - x)^3). - Ilya Gutkovskiy, May 10 2016

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