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A053400
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Number of 3-multigraphs on n nodes.
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7
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1, 4, 20, 276, 10688, 1601952, 892341888, 1799786093088, 13042490003160192, 341378170022783017472, 32526326484972756063585792, 11367103329997359707194173746176, 14669222110846093400698801891700529152
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OFFSET
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1,2
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REFERENCES
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F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY,1973.
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LINKS
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn,nice
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AUTHOR
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STATUS
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approved
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