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A165950
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Number of acyclic digraphs on n labeled nodes with one source and one sink.
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3
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1, 2, 12, 216, 10600, 1306620, 384471444, 261548825328, 402632012394000, 1381332938730123060, 10440873023366019273820, 172308823347127690038311496, 6163501139185639837183141411320, 474942255590583211554917995123517868, 78430816994991932467786587093292327531620
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OFFSET
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1,2
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..50
Antoine Genitrini, Martin Pépin, and Alfredo Viola, Unlabelled ordered DAGs and labelled DAGs: constructive enumeration and uniform random sampling, hal-03029381 [math.CO], [cs.DM], [cs.DS], 2020.
Ira Gessel, Counting Acyclic Digraphs by Sources and Sinks
Marcel et al., Is there a formula for the number of st-dags (DAG with 1 source and 1 sink) with n vertices?, MathOverflow, 2021.
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PROG
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(PARI) \\ see Marcel et al. link. B(n) is A003025 as vector.
B(n)={my(a=vector(n)); a[1]=1; for(n=2, #a, a[n]=sum(k=1, n-1, (-1)^(k-1)*binomial(n, k)*(2^(n-k)-1)^k*a[n-k])); a}
seq(n)={my(a=vector(n), b=B(n)); a[1]=1; for(n=2, #a, a[n]=sum(k=1, n-1, (-1)^(k-1) * binomial(n, k) * k * (2^(n-k)-1)^k * b[n-k])); a} \\ Andrew Howroyd, Jan 01 2022
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CROSSREFS
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The unlabeled version is A345258.
Cf. A003024, A003025, A049524.
Sequence in context: A153302 A123118 A182161 * A208651 A083667 A092124
Adjacent sequences: A165947 A165948 A165949 * A165951 A165952 A165953
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic, Oct 01 2009
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EXTENSIONS
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a(1)=1 inserted and terms a(13) and beyond from Andrew Howroyd, Jan 01 2022
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STATUS
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approved
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