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A372486
a(n) is the numerator of the probability that there is a survivor in "group Russian roulette" starting with n people.
5
1, 0, 3, 16, 15, 11704, 1105685, 11327177474, 244115733950627, 4354777045182131169523, 8214950835161136722829165047, 426292831687307296000152039222781332149, 7528468333926810743153269968816648803479402170227, 3337740693040652853366026406394437902927950280053024451402129
OFFSET
1,3
COMMENTS
See A372480 for more information.
LINKS
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
A372487 are the corresponding denominators.
Sequence in context: A195883 A272329 A076623 * A370978 A068516 A219508
KEYWORD
nonn,frac
AUTHOR
Hugo Pfoertner, May 04 2024
STATUS
approved