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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 Andrew Howroyd, Table of n, a(n) for n = 1..50 Harald Fripertinger, The cycle type of the induced action on 2-subsets Vladeta Jovovic, Formulae for the number T(n,k) of n-multigraphs on k nodes 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 Adjacent sequences: A053397 A053398 A053399 * A053401 A053402 A053403 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.)