A275597 - OEIS

A275597

Number of simple labeled graphs G on n vertices such that for each k in {1,2,...,n}, G has exactly k connected components and the vertices labeled with {1,2,...,k} are all in different components.

1, 2, 7, 52, 851, 28786, 1933879, 255839048, 66839167987, 34634544150646, 35712147523562999, 73426704068062929628, 301419821377908100819123, 2472253358027383404798964442, 40532633024489540112983979301783, 1328660090565074145503909701745941840

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..16.

Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, page 142.

EXAMPLE

a(3) = 7 because with 3 vertices there are four connected graphs, 1 2-3, 2 1-3, and the empty graph.

MATHEMATICA

nn = 16; Map[Total, Map[Select[#, # > 0 &] &, Transpose[ Map[Take[#, nn] &, Table[Clear[g]; g[z_] := Sum[2^Binomial[n, 2] z^n/n!, {n, 0, nn + k}]; Join[Table[0, {k - 1}], Range[0, nn]! CoefficientList[Series[D[Log[g[z]], z]^k, {z, 0, nn}], z]], {k, 1, nn}]]]]]

CROSSREFS

Row sums of A275595.

Sequence in context: A210856 A046662 A237195 * A118191 A005588 A106898

Adjacent sequences: A275594 A275595 A275596 * A275598 A275599 A275600

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Aug 03 2016

STATUS

approved