A234600 Denominators of the expectation of the process defined by randomly moving 2n balls between bins.

1, 3, 5, 105, 63, 1155, 6435, 45045, 85085, 2909907, 1322685, 111546435, 128707425, 717084225, 9704539845, 4512611027925, 265447707525, 501401225325, 8787716212275, 33393321606645

Offset

1,2

Comments

Start with two bins, one empty and the other containing 2n balls, n >= 1. Each turn, randomly select a ball and move it from the bin it is in to the other bin. Continue until both bins contain the same number of balls. The numbers in this sequence are the denominators of the rational expressions for the expected number of moves required to end up with the same number of balls in each bin.

Links

Table of n, a(n) for n=1..20.

Prog

(Maxima)
E(n) := (
    block (
        [T, P, S, i, t],
        T[0] : 1,
        T[1] : 1,
        for i : 2 thru n do (
            T[i] : T[i-1] - (n+i)*(n-i+1)*T[i-2]/(4*n^2)),
        P[n] : 1,
        for i : n - 1 step -1 thru 1 do (
            P[i] : (n+i+1)*P[i+1]/(2*n)),
        S : 0,
        for i : 1 thru n do (
            S : S + P[i]*T[i-1]/T[n]),
        disp(S)
    )
)$

Crossrefs

Cf. A233470 (numerators).

Sequence in context: A338269 A371194 A346710 * A003112 A130187 A289488

Adjacent sequences: A234597 A234598 A234599 * A234601 A234602 A234603

Keyword

nonn,frac

Author

Aaron Clark and Stephen Gueble, Apr 19 2014

Status

approved