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A000662
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Number of relations with 3 arguments on n nodes.
(Formerly M2180 N0872)
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7
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OFFSET
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1,1
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 76 (2.2.31)
W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = Sum_{1*s_1+2*s_2+...=n} (fixA[s_1, s_2,...]/(1^s_1*s_1!*2^s_2*s_2!*...)) where fixA[s_1, s_2, ...] = 2^Sum_{i, j, k>=1} (i*j*k*s_i*s_j*s_k/lcm(i, j, k)). - Christian G. Bower, Jan 06 2004
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PROG
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(Python)
from itertools import product
from math import factorial, prod, lcm
from fractions import Fraction
from sympy.utilities.iterables import partitions
def A000662(n): return int(sum(Fraction(1<<sum(r*s*t//lcm(r, s, t)*p[r]*p[s]*p[t] for r, s, t in product(p.keys(), repeat=3)), prod(q**p[q]*factorial(p[q]) for q in p)) for p in partitions(n))) # Chai Wah Wu, Jul 02 2024
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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