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A059166
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Number of n-node connected labeled graphs without endpoints.
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6
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1, 1, 0, 1, 10, 253, 12058, 1052443, 169488200, 51045018089, 29184193354806, 32122530765469967, 68867427921051098084, 290155706369032525823085, 2417761578629525173499004146, 40013923790443379076988789688611
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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FORMULA
| a(n)=Sum_{i=0..n} (-1)^i*binomial(n, i)*c(n-i)*(n-i)^i, for n>2, a(0)=1, a(1)=1, a(2)=0, where c(n) is number of n-node connected labeled graphs (Cf. A001187).
E.g.f.: 1+x^2/2+ln(Sum_{n >= 0} 2^binomial(n, 2)*(x*exp(-x))^n/n!).
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CROSSREFS
| Cf. A059167 (n-node labeled graphs without endpoints), A004108 (n-node connected unlabeled graphs without endpoints), A004110 (n-node unlabeled graphs without endpoints).
Sequence in context: A114450 A178689 A095983 * A100743 A126468 A024293
Adjacent sequences: A059163 A059164 A059165 * A059167 A059168 A059169
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 12 2001
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EXTENSIONS
| More terms from John Renze (jrenze(AT)yahoo.com), Feb 01 2001
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