login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A014500 Number of graphs with unlabeled (non-isolated) nodes and n labeled edges. 7
1, 1, 2, 9, 70, 794, 12055, 233238, 5556725, 158931613, 5350854707, 208746406117, 9315261027289, 470405726166241, 26636882237942128, 1678097862705130667, 116818375064650241036, 8932347052564257212796, 746244486452472386213939, 67796741482683128375533560 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

Peter Cameron, Thomas Prellberg, Dudley Stark, Asymptotic enumeration of 2-covers and line graphs, Discrete Math. 310 (2010), no. 2, 230-240 (see u_n).

G. Labelle, Counting enriched multigraphs..., Discrete Math., 217 (2000), 237-248.

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

FORMULA

E.g.f.: exp(-1+x/2)*Sum((1+x)^binomial(n, 2)/n!, n=0..infinity) [probably in the Labelle paper]. - Vladeta Jovovic, Apr 27 2004

E.g.f.: exp(x/2)*Sum(A020556(n)*(log(1+x)/2)^n/n!, n=0..infinity). - Vladeta Jovovic, May 02 2004

Binomial transform of A060053.

The e.g.f.'s of A020554 (S(x)) and A014500 (U(x)) are related by S(x) = U(e^x-1).

The e.g.f.'s of A014500 (U(x)) and A060053 (V(x)) are related by U(x) = e^x*V(x).

MAPLE

read("transforms") ;

A020556 := proc(n) local k; add((-1)^(n+k)*binomial(n, k)*combinat[bell](n+k), k=0..n) end proc:

A014500 := proc(n) local i, gexp, lexp;

gexp := [seq(1/2^i/i!, i=0..n+1)] ;

lexp := add( A020556(i)*((log(1+x))/2)^i/i!, i=0..n+1) ;

lexp := taylor(lexp, x=0, n+1) ;

lexp := gfun[seriestolist](lexp, 'ogf') ;

CONV(gexp, lexp) ; op(n+1, %)*n! ; end proc:

seq(A014500(n), n=0..20) ; # R. J. Mathar, Jul 03 2011

MATHEMATICA

max = 20; A020556[n_] := Sum[(-1)^(n+k)*Binomial[n, k]*BellB[n+k], {k, 0, n}]; egf = Exp[x/2]*Sum[A020556[n]*(Log[1+x]/2)^n/n!, {n, 0, max}] + O[x]^max; CoefficientList[egf, x]*Range[0, max-1]! (* Jean-François Alcover, Feb 19 2017, after Vladeta Jovovic *)

CROSSREFS

Cf. A020554, A020555, A014501, A060053.

Sequence in context: A201862 A167016 A108522 * A101482 A099717 A177450

Adjacent sequences:  A014497 A014498 A014499 * A014501 A014502 A014503

KEYWORD

nonn

AUTHOR

Simon Plouffe, Gilbert Labelle (gilbert(AT)lacim.uqam.ca)

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 22 09:19 EDT 2017. Contains 292336 sequences.