OFFSET
0,3
COMMENTS
Also 1 together with the row sums of A046860.
A binary relation R on [n] is periodic iff there is a d>=2 such that R^d = R. Let A be the class of non-arcless strongly connected periodic relations (A000629). Then a(n) is the number of binary relations on [n] whose strongly connected components are in A. - Geoffrey Critzer, Dec 12 2023
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..77
FORMULA
Sum_{n>=0} a_n*x^n/(n!*2^C(n,2)) = 1/(2-Sum_{n>=0} x^n/(n!*2^C(n,2))).
MAPLE
b:= proc(n, k) option remember; `if`([n, k]=[0$2], 1,
add(binomial(n, r)*2^(r*(n-r))*b(r, k-1), r=0..n-1))
end:
a:= n-> add(b(n, k), k=0..n):
seq(a(n), n=0..15); # Alois P. Heinz, Apr 21 2020
MATHEMATICA
nn = 15; e2[x_] := Sum[x^n/(n! 2^Binomial[n, 2]), {n, 0, nn}];
Table[n! 2^Binomial[n, 2], {n, 0, nn}] CoefficientList[Series[1/(1 - (e2[x] - 1)), {x, 0, nn}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Apr 21 2020
STATUS
approved