A267634 Total number of nodes in a maximal connected component over all simple labeled graphs on n nodes.

0, 1, 3, 19, 219, 4691, 188215, 14388823, 2128027015, 615859881223, 351128005027151, 395921495115621487, 885006516085472323279, 3928043932547284205971407, 34658076266993991201736109023, 608435086028952410310283975943071

Offset

0,3

Comments

In other words, a(n) is the total number of nodes in one maximal component of each of the graphs in A006125.

Links

Table of n, a(n) for n=0..15.

Mathematica

nn = 15; a = Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}]; b =
Total[(Range[0, nn]! CoefficientList[Series[ Log[a], {x, 0, nn}],
      x]) Table[x^i/i!, {i, 0, nn}]]; Map[Total, Transpose[
  Table[Range[0, nn]! CoefficientList[Series[n (Exp[b[[1 ;; n]]] - Exp[b[[1 ;; n - 1]]]), {x, 0, nn}], x], {n, 1, nn}]]]

Crossrefs

Cf. A006125.

Sequence in context: A378326 A001833 A001035 * A277407 A271587 A382450

Adjacent sequences: A267631 A267632 A267633 * A267635 A267636 A267637

Keyword

nonn

Author

Geoffrey Critzer, Jan 18 2016

Status

approved