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A053549
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Number of labeled rooted connected graphs.
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7
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0, 1, 2, 12, 152, 3640, 160224, 13063792, 2012388736, 596666619648, 344964885948160, 392058233038486784, 880255154481199466496, 3916538634445633156373504, 34603083354426212294072477696, 607915214065957203519146330173440
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 10, R_p.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.20, G(x).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..50
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FORMULA
| E.g.f.: Sum(2^binomial(n, 2)*x^n/(n-1)!, n=1..infinity)/Sum(2^binomial(n, 2)*x^n/n!, n=0..infinity).
a(n) = n * A001187(n).
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MAPLE
| add(2^binomial(n, 2)*x^n/(n-1)!, n=1..31)/add(2^binomial(n, 2)*x^n/n!, n=0..31);
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MATHEMATICA
| f[x_, lim_] := Sum[2^Binomial[n, 2]*x^n/(n - 1)!, {n, 1, lim}] / Sum[2^Binomial[n, 2]*x^n/n!, {n, 0, lim}]; nn = 15; Range[0, nn]! CoefficientList[Series[f[x, nn], {x, 0, nn}], x] (* T. D. Noe, Oct 21 2011 *)
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CROSSREFS
| Cf. A006125.
Sequence in context: A000795 A085628 A177777 * A139383 A130529 A075631
Adjacent sequences: A053546 A053547 A053548 * A053550 A053551 A053552
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 16 2000
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