OFFSET
1,2
REFERENCES
M. D. McIlroy, Calculation of numbers of structures of relations on finite sets, Massachusetts Institute of Technology, Research Laboratory of Electronics, Quarterly Progress Reports, No. 17, Sept. 15, 1955, pp. 14-22.
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).
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..59
R. L. Davis, The number of structures of finite relations, Proc. Amer. Math. Soc. 4 (1953), 486-495.
M. D. McIlroy, Calculation of numbers of structures of relations on finite sets, Massachusetts Institute of Technology, Research Laboratory of Electronics, Quarterly Progress Reports, No. 17, Sep. 15, 1955, pp. 14-22. [Annotated scanned copy]
W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.
FORMULA
a(n) = A000595(n)/2. - Sean A. Irvine, Mar 16 2012
MATHEMATICA
permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];
edges[v_] := Sum[2 GCD[v[[i]], v[[j]]], {i, 2, Length[v]}, {j, 1, i - 1}] + Total[v];
a[n_] := Module[{s = 0}, Do[s += permcount[p]*2^edges[p], {p, IntegerPartitions[n]}]; s/(2 n!)];
PROG
(Python)
from itertools import product
from math import prod, factorial, gcd
from fractions import Fraction
from sympy.utilities.iterables import partitions
def A001173(n): return int(sum(Fraction(1<<sum(p[r]*p[s]*gcd(r, s) for r, s in product(p.keys(), repeat=2)), prod(q**p[q]*factorial(p[q]) for q in p)) for p in partitions(n)))>>1 # Chai Wah Wu, Jul 02 2024
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Apr 18 2000
a(13)-a(14) (based on A000595) from Pontus von Brömssen, Aug 04 2022
STATUS
approved