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 A366166 Decimal expansion of sqrt(Pi)/(3*sqrt(3))*(Gamma(1/3)/Gamma(5/6))^3. 3
 4, 5, 5, 9, 7, 9, 4, 4, 9, 9, 9, 5, 9, 8, 4, 5, 8, 1, 5, 4, 8, 1, 7, 3, 6, 4, 8, 4, 5, 5, 7, 2, 4, 8, 1, 1, 7, 6, 3, 6, 7, 4, 2, 3, 8, 0, 1, 6, 6, 1, 4, 0, 5, 6, 3, 5, 0, 5, 1, 8, 3, 8, 7, 6, 5, 4, 7, 2, 1, 1, 5, 9, 5, 9, 3, 5, 5, 7, 0, 4, 4, 9, 2, 3, 2, 4, 8, 7, 9, 6 (list; constant; graph; refs; listen; history; text; internal format)
 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 Cf. A059231, A366566, A366567. Sequence in context: A268604 A246823 A088245 * A154857 A019314 A335820 Adjacent sequences: A366163 A366164 A366165 * A366167 A366168 A366169 KEYWORD nonn,cons AUTHOR Hugo Pfoertner, Oct 13 2023 STATUS approved

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Last modified April 21 01:42 EDT 2024. Contains 371850 sequences. (Running on oeis4.)