A054918 Number of connected unlabeled digraphs with n nodes such that complement is also connected.

1, 1, 10, 180, 9120, 1520742, 878908844, 1791588717764, 13024366540532952, 341234368845828951004, 32522226812040344643993088, 11366680383641301437820379768750, 14669062959091969068110415719779627436

Offset

1,3

Links

Andrew Howroyd, Table of n, a(n) for n = 1..50

V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

Formula

a(n) = 2*A003085(n) - A000273(n).

Mathematica

A000273 = Cases[Import["https://oeis.org/A000273/b000273.txt", "Table"], {_, _}][[All, 2]];
A003085 = Cases[Import["https://oeis.org/A003085/b003085.txt", "Table"], {_, _}][[All, 2]];
a[n_] := 2*A003085[[n]] - A000273[[n + 1]];
Array[a, 50] (* Jean-François Alcover, Aug 31 2019 *)

Prog

(Python)
from functools import lru_cache
from itertools import product, combinations
from fractions import Fraction
from math import prod, gcd, factorial
from sympy import mobius, divisors
from sympy.utilities.iterables import partitions
def A054918(n):
    @lru_cache(maxsize=None)
    def b(n): return int(sum(Fraction(1<<sum(p[r]*p[s]*gcd(r, s)<<1 for r, s in combinations(p.keys(), 2))+sum(r*(q*r-1) for q, r in p.items()), prod(q**r*factorial(r) for q, r in p.items())) for p in partitions(n)))
    @lru_cache(maxsize=None)
    def c(n): return n*b(n)-sum(c(k)*b(n-k) for k in range(1, n))
    return (sum(mobius(n//d)*c(d) for d in divisors(n, generator=True))//n<<1)-b(n) # Chai Wah Wu, Jul 05 2024

Crossrefs

Cf. A000273, A003085.

Sequence in context: A034908 A030048 A318796 * A095807 A064092 A171513

Adjacent sequences: A054915 A054916 A054917 * A054919 A054920 A054921

Keyword

nonn,easy

Author

N. J. A. Sloane, May 24 2000

Extensions

More terms from Vladeta Jovovic, Jul 19 2000

Status

approved