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 A165950 Number of acyclic digraphs on n labeled nodes with one source and one sink. 3
 1, 2, 12, 216, 10600, 1306620, 384471444, 261548825328, 402632012394000, 1381332938730123060, 10440873023366019273820, 172308823347127690038311496, 6163501139185639837183141411320, 474942255590583211554917995123517868, 78430816994991932467786587093292327531620 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS 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. PROG (PARI) \\ see Marcel et al. link. B(n) is A003025 as vector. B(n)={my(a=vector(n)); a=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; 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 CROSSREFS 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 KEYWORD nonn AUTHOR Vladeta Jovovic, Oct 01 2009 EXTENSIONS a(1)=1 inserted and terms a(13) and beyond from Andrew Howroyd, Jan 01 2022 STATUS approved

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Last modified March 24 04:28 EDT 2023. Contains 361454 sequences. (Running on oeis4.)