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A129271
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Number of labeled n-node connected graphs with at most one cycle.
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3
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1, 1, 1, 4, 31, 347, 4956, 85102, 1698712, 38562309, 980107840, 27559801736, 849285938304, 28459975589311, 1030366840792576, 40079074477640850, 1666985134587145216
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| The majority of those graphs of order 4 are trees since we have 16 trees and only 9 unicycles. See example.
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REFERENCES
| J. Riordan, An Introduction to Combinatorial Analysis, Dover, 2002, p. 2.
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LINKS
| Wikipedia, PseudoForest.
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FORMULA
| a(0) = 1, for n >=1, a(n) = A000272(n) + A057500(n) = n^{n-2} + (n-1)(n-2)/2Sum_{r=1..n-2}( (n-3)!/(n-2-r)! )n^(n-2-r)
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EXAMPLE
| a(4) = 16 + 3*3 = 31.
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CROSSREFS
| Cf. A129137, A005703, A000272, A057500.
Sequence in context: A122400 A107725 A145160 * A136728 A102757 A145561
Adjacent sequences: A129268 A129269 A129270 * A129272 A129273 A129274
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KEYWORD
| easy,nonn
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AUTHOR
| Washington Bomfim (webonfim(AT)bol.com.br), May 10 2008
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