The list below are the first 12 terms in the sequence

number of 3-deck sets of cards with n cards each that are "sucker's bets" i.\
    e.

   deck A beats deck B, deck B beats deck C and deck C beats deck A. See the

                     article "a Treatise on Sucker's bets"

  http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/suckerbets.html

[0, 0, 15, 39, 5196, 32115, 2093199, 19618353, 960165789, 11272949151,

    479538890271, 6504453085104]

            Up to cyclic synmmetry, (i.e. dividing the above by 3):

[0, 0, 5, 13, 1732, 10705, 697733, 6539451, 320055263, 3757649717, 159846296757,

    2168151028368]

                        The sequence of probabilities is



               13     433    10705    697733     2179817     29095933
[0, 0, 1/112, -----, -----, -------, ---------, ----------, ----------,
              11550  63063  5717712  133024320  1051723530  6905255500

     3757649717     7611728417     151069609
    -------------, -------------, -----------]
    1850332263780  2167095166080  78612313325



                             and in floating point



[0., 0., 0.008928571429, 0.001125541126, 0.006866149723, 0.001872252397,

    0.005245153668, 0.002072614083, 0.004213592531, 0.002030797274,

    0.003512410777, 0.001921704153]