cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A093351 Number of labeled n-vertex graphs with a 2-component.

Original entry on oeis.org

0, 0, 1, 3, 9, 65, 885, 20769, 904799, 75119535, 12059144775, 3777502008115, 2321770382163177, 2810098818045932049, 6714509196242295683053, 31734155232117923771498025, 297105206555826680431032956415
Offset: 0

Views

Author

Goran Kilibarda, Vladeta Jovovic, Apr 26 2004

Keywords

Crossrefs

Cf. A093352.

Formula

E.g.f.: (1-exp(-x^2/2))*Sum(2^binomial(n, 2)*x^n/n!, n=0..infinity).

A093377 Number of labeled n-vertex graphs without 2-components and without isolated vertices (1-components).

Original entry on oeis.org

1, 0, 0, 4, 38, 728, 26864, 1871576, 251762204, 66308767200, 34497665550400, 35641856042561008, 73354660691960203016, 301272244237002052739424, 2471648864359822034978330304, 40527681073171940835893232576032
Offset: 0

Views

Author

Goran Kilibarda, Vladeta Jovovic, Apr 28 2004

Keywords

Comments

Also number of unlabeled n-block ordered r-bicoverings, cf. A060053. - Vladeta Jovovic, May 13 2004

Crossrefs

Programs

  • Mathematica
    nn=20;g=Sum[2^Binomial[n,2]x^n/n!,{n,0,nn}];Range[0,nn]!CoefficientList[Series[Exp[ Log[g]-x-x^2/2!],{x,0,nn}],x]  (* Geoffrey Critzer, Apr 15 2013 *)
  • PARI
    N=66; x='x+O('x^N);
    egf=exp(-x-x^2/2)*sum(i=0,N, 2^binomial(i, 2)*x^i/i!);
    Vec(serlaplace(egf))
    /* Joerg Arndt, Jul 06 2011 */

Formula

E.g.f.: exp(-x-x^2/2)*Sum_{n>=0} 2^binomial(n, 2)*x^n/n!.
Inverse binomial transform of A093352().

A228596 The number of simple labeled graphs on n nodes with no components of size 3.

Original entry on oeis.org

1, 1, 2, 4, 48, 944, 32288, 2089312, 268215040, 68708556288, 35183367427072, 36028619925285888, 73786915826515503104, 302231414653310649337856, 2475880026112961032035266560, 40564819073011099018919903485952, 1329227995107917459000217502447435776
Offset: 0

Views

Author

Geoffrey Critzer, Aug 27 2013

Keywords

Crossrefs

Programs

  • Mathematica
    nn = 15; g = Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}];
    Range[0, nn]! CoefficientList[Series[Exp[-4 x^3/3!] g, {x, 0, nn}], x]

Formula

E.g.f.: exp(-4*x^3/3!)*A(x) where A(x) is the e.g.f. for A006125.
Generally, the e.g.f. for the number of simple labeled graphs on n nodes with no size k components is exp( -A001187(k)*x^k/k! ) * A(x) with A(x) as above.

A093376 Number of labeled n-vertex graphs with 2-components and without isolated vertices(1-components).

Original entry on oeis.org

0, 0, 1, 0, 3, 40, 585, 15708, 760277, 67656960, 11346344145, 3648840170580, 2277220167519825, 2780207051899228224, 6675377730807161508041, 31633731603265107184483860, 296598264243770222308892404305
Offset: 0

Views

Author

Goran Kilibarda, Vladeta Jovovic, Apr 28 2004

Keywords

Crossrefs

Formula

E.g.f. exp(-x)*(1-exp(-x^2/2))*Sum(2^binomial(n, 2)*x^n/n!, n=0..infinity). Inverse binomial transform of A093351().
Showing 1-4 of 4 results.