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A059167
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Number of n-node labeled graphs without endpoints.
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9
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1, 1, 1, 2, 15, 314, 13757, 1142968, 178281041, 52610850316, 29702573255587, 32446427369694348, 69254848513798160815, 291053505824567573585744, 2421830049319361003822380177, 40050220743831370293688592267252
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 31, problem 1.16(a).
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FORMULA
| a(n)=Sum_{i=0..n-1} binomial(n-1, i)*b(i+1)*a(n-i-1), n>0, a(0)=1, where b(n) is number of n-node connected labeled graphs without endpoints (Cf. A059166).
E.g.f.: exp(1/2*x^2)*Sum(2^binomial(n, 2)*(x/exp(x))^n/n!, n = 0 .. infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 23 2004
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CROSSREFS
| Cf. A059166 (n-node connected labeled graphs without endpoints), A004108 (n-node connected unlabeled graphs without endpoints), A004110 (n-node unlabeled graphs without endpoints).
Sequence in context: A174482 A076111 A087526 * A003025 A015200 A030642
Adjacent sequences: A059164 A059165 A059166 * A059168 A059169 A059170
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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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