A372486 a(n) is the numerator of the probability that there is a survivor in "group Russian roulette" starting with n people.

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, 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

A372487 are the corresponding denominators.

Cf. A372480, A372481.

Sequence in context: A195883 A272329 A076623 * A370978 A068516 A219508

Adjacent sequences: A372483 A372484 A372485 * A372487 A372488 A372489

Keyword

nonn,frac

Author

Hugo Pfoertner, May 04 2024

Status

approved