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
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
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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 *)
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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 */
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
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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]
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
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