OFFSET
1,1
COMMENTS
This constant c occurs in the probability that the "big player" in a game with 3 gamblers goes broke first, although he starts with an initial capital of N-2 units, whereas the other two gamblers start with one unit each. This probability is ~ c/N^3. See Diaconis link for details.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
Persi Diaconis, Gambler's ruin with k gamblers (slide 3), talk in the Rutgers Experimental Mathematics Seminar, Fall 2023 Semester, Oct. 12, 2023.
FORMULA
Equals Gamma(1/3)^9 / (2*Pi)^4. - Peter Luschny, Oct 13 2023
EXAMPLE
4.5597944999598458154817364845572481176367423801661405635...
MATHEMATICA
First[RealDigits[Gamma[1/3]^9/(2Pi)^4, 10, 100]] (* Paolo Xausa, Oct 14 2023 *)
PROG
(PARI) sqrt(Pi)/(3*sqrt(3))*(gamma(1/3)/gamma(5/6))^3
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Oct 13 2023
STATUS
approved