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A053400 Number of 3-multigraphs on n nodes. 7
1, 4, 20, 276, 10688, 1601952, 892341888, 1799786093088, 13042490003160192, 341378170022783017472, 32526326484972756063585792, 11367103329997359707194173746176, 14669222110846093400698801891700529152 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY,1973.
LINKS
PROG
(Python)
from itertools import combinations
from math import prod, gcd, factorial
from fractions import Fraction
from sympy.utilities.iterables import partitions
def A053400(n): return int(sum(Fraction(1<<(sum(p[r]*p[s]*gcd(r, s) for r, s in combinations(p.keys(), 2))+sum((q>>1)*r+(q*r*(r-1)>>1) for q, r in p.items())<<1), prod(q**r*factorial(r) for q, r in p.items())) for p in partitions(n))) # Chai Wah Wu, Jul 09 2024
CROSSREFS
Column k=3 of A063841.
Cf. A004102.
Sequence in context: A000847 A188810 A120443 * A362259 A120599 A012797
KEYWORD
easy,nonn,nice
AUTHOR
Vladeta Jovovic, Jan 06 2000
STATUS
approved

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Last modified July 25 14:35 EDT 2024. Contains 374609 sequences. (Running on oeis4.)