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A215851
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Number of simple labeled graphs on n nodes with exactly 1 connected component that is a tree or a cycle.
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3
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1, 1, 4, 19, 137, 1356, 17167, 264664, 4803129, 100181440, 2359762091, 61937322624, 1792399894837, 56697025885696, 1946238657504975, 72058247875111936, 2862433512904759793, 121439708940308299776, 5480390058971655049939, 262144060822550204416000
(list;
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listen;
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internal format)
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OFFSET
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1,3
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LINKS
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FORMULA
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a(1) = a(2) = 1, a(n) = A000272(n) + A001710(n-1) = n^(n-2) + (n-1)!/2 for n>2.
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EXAMPLE
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a(3) = 4:
.1-2. .1-2. .1-2. .1 2.
.|/ . .| . . / . .|/ .
.3... .3... .3... .3...
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MAPLE
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a:= n-> `if`(n<3, 1, (n-1)!/2+n^(n-2)):
seq(a(n), n=1..25);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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