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A197927 The number of isolated nodes in all labeled directed graphs (with self loops allowed) on n nodes. 2
0, 1, 4, 48, 2048, 327680, 201326592, 481036337152, 4503599627370496, 166020696663385964544, 24178516392292583494123520, 13944156602510523416463735259136, 31901471898837980949691369446728269824, 289909687580898100839964337544428699577745408 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Here, isolated means indegree = outdegree = 0.

LINKS

Table of n, a(n) for n=0..13.

FORMULA

E.g.f.: x*A(x) where A(x) = Sum_{n>=0} 2^(n^2) x^n/n!.

a(n) = n * 2^((n-1)^2) = n*A002416(n-1).

MATHEMATICA

a = Sum[2^(n^2)x^n/n!, {n, 0, 20}]; Range[0, 12]! CoefficientList[Series[x a, {x, 0, 12}], x]

CROSSREFS

Sequence in context: A013150 A332865 A011266 * A100568 A112693 A239162

Adjacent sequences:  A197924 A197925 A197926 * A197928 A197929 A197930

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Oct 19 2011

STATUS

approved

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Last modified June 22 17:18 EDT 2021. Contains 345388 sequences. (Running on oeis4.)