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A329426
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Number of non-isomorphic directed graphs where every vertex has outdegree 1, and no self-loops.
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3
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1, 2, 6, 20, 97, 550, 3794, 29826, 266527, 2649156, 29040865, 347548542, 4509961264, 63050417976, 944767674590, 15103712944100, 256594870255076, 4616238126871328, 87670085904641440, 1752759735606185804, 36796608121601906104, 809312755145598475440, 18609995953274373396982
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OFFSET
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2,2
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LINKS
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FORMULA
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a(n) = 1 + A056542(n-1) + Sum_{2..floor(n/2)} a(i)*a(n-i).
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EXAMPLE
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For n = 2, a(2) = 1 + A329427(2) + A056542(1) = 1 + 0 + 0 = 1, which is the graph A <--> B.
For n = 3, a(3) = 1 + A329427(3) + A056542(2) = 1 + 0 + 1 = 2, which are graphs A --> B <--> C and A --> B --> C --> A.
The middle term is nonzero when there are graphs with more than 1 component.
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PROG
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(Kotlin)
fun A329427(n: Long): Long = (2L..(n/2)).map { a(it) * a(n-it) }.sum()
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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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