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

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

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..50

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.

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]

Crossrefs

Cf. A093352, A006129.

Sequence in context: A143968 A308665 A097424 * A032019 A181179 A175814

Adjacent sequences: A228593 A228594 A228595 * A228597 A228598 A228599

Keyword

nonn

Author

Geoffrey Critzer, Aug 27 2013

Status

approved