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A003086 Number of self-complementary digraphs with n nodes.
(Formerly M3404)
8
1, 1, 4, 10, 136, 720, 44224, 703760, 179228736, 9168331776, 9383939974144, 1601371799340544, 6558936236286040064, 3837878966366932639744, 62879572771326489528942592, 128777257564337108286016980992 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, pp. 140, 243.

R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..80

MATHEMATICA

Table[GraphPolynomial[n, x, Directed]/.x -> -1, {n, 1, 20}]  (* Geoffrey Critzer, Oct 21 2012 *)

PROG

(PARI)

permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}

edges(v) = {4*sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, 2*v[i]-1)}

a(n) = {my(s=0); forpart(p=n\2, s+=permcount(2*Vec(p))*2^edges(p)*if(n%2, n*4^#p, 1)); s/n!} \\ Andrew Howroyd, Sep 16 2018

CROSSREFS

Cf. A000171, A002785.

Sequence in context: A203224 A198156 A273517 * A102958 A220197 A299880

Adjacent sequences:  A003083 A003084 A003085 * A003087 A003088 A003089

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from R. C. Read (rcread(AT)math.uwaterloo.ca) and Vladeta Jovovic.

STATUS

approved

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Last modified November 14 16:58 EST 2018. Contains 317210 sequences. (Running on oeis4.)