A182100 The number of connected simple labeled graphs with <= n nodes.

1, 2, 4, 11, 65, 974, 31744, 2069971, 267270041, 68629753650, 35171000942708, 36024807353574291, 73784587576805254665, 302228602363365451957806, 2475873310144021668263093216, 40564787336902311168400640561099

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..80

Formula

a(n) = Sum_{i=0..n} binomial(n,i)*A001187(i).

E.g.f.: exp(x)*A(x) where A(x) is e.g.f. for A001187.

a(n) = A327078(n) + n. - Gus Wiseman, Sep 03 2019

Example

From Gus Wiseman, Sep 03 2019: (Start)
The a(0) = 1 through a(3) = 11 edge-sets (singletons represent uncovered vertices):
  {}  {}     {}       {}
      {{1}}  {{1}}    {{1}}
             {{2}}    {{2}}
             {{1,2}}  {{3}}
                      {{1,2}}
                      {{1,3}}
                      {{2,3}}
                      {{1,2},{1,3}}
                      {{1,2},{2,3}}
                      {{1,3},{2,3}}
                      {{1,2},{1,3},{2,3}}
(End)

Mathematica

nn = 15; g = Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[Exp[x] (Log[g] + 1), {x, 0, nn}], x]

Crossrefs

The unlabeled version is A292300(n) + 1.

Cf. A001187, A006129, A054592, A287689, A327070, A327075, A327078.

Sequence in context: A351184 A156434 A007903 * A327484 A006894 A193565

Adjacent sequences: A182097 A182098 A182099 * A182101 A182102 A182103

Keyword

nonn

Author

Geoffrey Critzer, Apr 11 2012

Status

approved