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Number of relations with 4 arguments on n nodes.
(Formerly M2189 N0875)
3

%I M2189 N0875 #37 Jul 02 2024 15:12:10

%S 2,32896,402975273205975947935744,

%T 4824670384888174809315457708695329515706856139873561594988392833332671414272

%N Number of relations with 4 arguments on n nodes.

%D W. Oberschelp, "Strukturzahlen in endlichen Relationssystemen", in Contributions to Mathematical Logic (Proceedings 1966 Hanover Colloquium), pp. 199-213, North-Holland Publ., Amsterdam, 1968.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A001377/b001377.txt">Table of n, a(n) for n = 1..7</a>

%H P. J. Cameron, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/groups.html">Sequences realized by oligomorphic permutation groups</a>, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

%H W. Oberschelp, <a href="/A000662/a000662.pdf">Strukturzahlen in endlichen Relationssystemen</a>, in Contributions to Mathematical Logic (Proceedings 1966 Hanover Colloquium), pp. 199-213, North-Holland Publ., Amsterdam, 1968. [Annotated scanned copy]

%o (Python)

%o from itertools import product

%o from math import factorial, prod, lcm

%o from fractions import Fraction

%o from sympy.utilities.iterables import partitions

%o def A001377(n): return int(sum(Fraction(1<<sum(prod(r)//lcm(*r)*prod(p[d] for d in r) for r in product(p.keys(),repeat=4)),prod(q**p[q]*factorial(p[q]) for q in p)) for p in partitions(n))) # _Chai Wah Wu_, Jul 02 2024

%Y Cf. A000595, A000662, A051241.

%K nonn,nice

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Vladeta Jovovic_