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A054918
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Number of connected unlabeled digraphs with n nodes such that complement is also connected.
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1
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1, 1, 10, 180, 9120, 1520742, 878908844, 1791588717764, 13024366540532952, 341234368845828951004, 32522226812040344643993088, 11366680383641301437820379768750, 14669062959091969068110415719779627436
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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FORMULA
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MATHEMATICA
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A000273 = Cases[Import["https://oeis.org/A000273/b000273.txt", "Table"], {_, _}][[All, 2]];
A003085 = Cases[Import["https://oeis.org/A003085/b003085.txt", "Table"], {_, _}][[All, 2]];
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PROG
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(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
@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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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