A356746 Number of 2-colored labeled directed acyclic graphs on n nodes such that all black nodes are sources.

1, 2, 8, 74, 1664, 90722, 11756288, 3544044674, 2439773425664, 3777981938265602, 12999312305021800448, 98399334883456516073474, 1625096032161083727093530624, 58150966795467956854830216929282

Offset

0,2

Comments

A source is a vertex with in-degree equal to 0. There may be white sources as well.

Links

Table of n, a(n) for n=0..13.

Valery A. Liskovets, More on counting acyclic digraphs, arXiv:0804.2496 [math.CO], 2008.

Formula

a(n) = sum_{t=0..n}binomial(n,t)*2^(t(n-t))*A003024(t).

Let E(x) = sum_{n>=0}x^n/(2^n*n!). Then sum_{n>=0}a(n)x^n/(2^n*n!) = E(x)/E(-x).

a(n) = sum_{k=0..n}|A224069(n,k)|.

Mathematica

nn = 13; B[n_, q_] := q^Binomial[n, 2] n!; e[u_, q_] := Sum[u^n/B[n, q], {n, 0, nn}]; Table[B[n, 2], {n, 0, nn}] CoefficientList[Series[e[u, 2]/e[-u, 2], {u, 0, nn}], u]

Crossrefs

Cf. A003024

Sequence in context: A064605 A356108 A295373 * A132039 A204552 A002668

Adjacent sequences: A356743 A356744 A356745 * A356747 A356748 A356749

Keyword

nonn

Author

Geoffrey Critzer, Oct 08 2022

Status

approved