A228596 - OEIS

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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

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

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