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.
MATHEMATICA
nn = 10; B[n_] := n! 2^Binomial[n, 2]; e[z_] := Sum[z^n/B[n], {n, 0, nn}];
egf[ggf_] := Normal[Series[ggf, {z, 0, nn}]] /. Table[z^i -> z^i*2^Binomial[i, 2], {i, 1, nn + 1}]; Map[ Coefficient[#, u v] &, Table[n!, {n, 0, nn}] CoefficientList[ Series[Exp[(u - 1) (v - 1) z] egf[e[(u - 1) z]*1/e[-z]*e[(v - 1) z]], {z, 0, nn}], z]] (* Geoffrey Critzer, Apr 15 2023 *)
PROG
(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
CROSSREFS
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