A217652 Number of isolated nodes over all labeled directed graphs on n nodes.

0, 1, 2, 12, 256, 20480, 6291456, 7516192768, 35184372088832, 648518346341351424, 47223664828696452136960, 13617340432139183023890366464, 15576890575604482885591488987660288, 70778732319555200400381918345807787982848

Offset: 0

Author

Geoffrey Critzer, Oct 09 2012

Keywords

• nonn

Comments

a(n) = Sum_{k=1..n} A217580(n,k) * k.

a(n) is also the number of labeled directed graphs on n nodes with an "Emperor". - Rémy-Robert Joseph, Nov 12 2012

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..40

Crossrefs

See also A123903 (case of tournaments) and A219116 (case of semicomplete digraphs) Rémy-Robert Joseph, Nov 12 2012

Programs

Maple

a:= n-> 2^(n^2-3*n+2)*n:
seq (a(n), n=0..15);  # Alois P. Heinz, Oct 09 2012

Mathematica

nn=15; s=Sum[2^(n^2-n)x^n/n!,{n,0,nn}]; Range[0,nn]! CoefficientList[Series[x s, {x,0,nn}], x]

Maxima

A217652(n):=2^(n^2-3*n+2)*n$ makelist(A217652(n),n,0,10); /* Martin Ettl, Nov 13 2012 */

Formula

E.g.f.: x * A(x) where A(x) is the e.g.f. for A053763.

a(n) = 2^(n^2-3*n+2)*n. - Alois P. Heinz, Oct 09 2012