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A272582 The number of strongly connected digraphs with n vertices and n+1 edges. 0
0, 9, 84, 720, 6480, 63000, 665280, 7620480, 94348800, 1257379200, 17962560000, 273988915200, 4446092851200, 76498950528000, 1391365527552000, 26676557107200000, 537799391281152000, 11373816888225792000, 251805357846282240000, 5824367407574876160000 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

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

Table of n, a(n) for n=2..21.

E. M. Wright, Formulae for the number of sparsely-edged strong labelled digraphs, Quart. J. Math. 28 (3) (1977) 363-367, Section 3.

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

MATHEMATICA

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

PROG

(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

CROSSREFS

Sequence in context: A242596 A180807 A203455 * A037595 A037686 A181353

Adjacent sequences:  A272579 A272580 A272581 * A272583 A272584 A272585

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, May 10 2016

STATUS

approved

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Last modified September 23 02:44 EDT 2020. Contains 337291 sequences. (Running on oeis4.)