OFFSET
1,3
COMMENTS
See A372480 for more information.
LINKS
Hugo Pfoertner, Table of n, a(n) for n = 1..41
Hugo Pfoertner, Plot of probability vs n, using Plot 2.
EXAMPLE
a(n)/A372487(n): 1, 0, 3/4, 16/27, 15/32, 11704/28125, 1105685/2519424, 11327177474/23162146875, 244115733950627/458647142400000, ...
Approximately 1.0, 0.0, 0.75, 0.59259, 0.46875, 0.41614, 0.43886, 0.48904, 0.53225, 0.55475, 0.55678, 0.54455, 0.52521, 0.50453, 0.48639, 0.47290, 0.46485, 0.46208, 0.46390, 0.46931, 0.47724, 0.48664, 0.49657, 0.50627, 0.51514, ...
PROG
(PARI) P(n, k) = {my (nmk=n-k); binomial(n, k) * (1/(n-1)^n) * sum (r=0, nmk-2, (-1)^r * binomial(nmk, r) * (nmk-r)^(k+r) * (nmk-r-1)^(nmk-r))};
a372486_7(m) = {my (p=vector(m)); p[1]=1; p[2]=0; for (n=3, m, p[n] = sum (k=1, n-2, P(n, k)*p[k])); p};
apply (x->numerator(x), a372486_7(14))
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Hugo Pfoertner, May 04 2024
STATUS
approved