A003127 Value of an urn with n balls of type -1 and n balls of type +1. (Formerly M3537)

0, 1, 4, 17, 70, 282, 1136, 4583, 18457, 74131, 296945, 1190344, 4773949, 19145523, 76751393, 307503585, 1231182078, 4929075135, 19736248104, 79031964989, 316476142454, 1267191674419, 5073155081395, 20306187559891, 81265371486027

Offset

1,3

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..25.

W. M. Boyce, On a simple optimal stopping problem, Discr. Math., 5 (1973), 297-312.

Formula

a(n) = B(n, n) where B(n, m) is defined in A003125. - Sean A. Irvine, Feb 02 2015

Mathematica

w[a_, 0] = a; w[0, b_] = 0; w[a_, b_] := w[a, b] = Max[ (a(1 + w[a-1, b]) + b(-1 + w[a, b-1])) / (a+b), 0]; Table[w[n, n] * Binomial[2n, n], {n, 0, 40}] (* Joel B. Lewis, Aug 27 2009 *)

Crossrefs

Sequence in context: A339065 A005511 A349695 * A172447 A291009 A017955

Adjacent sequences: A003124 A003125 A003126 * A003128 A003129 A003130

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Joel B. Lewis, Aug 27 2009

Title clarified by Sean A. Irvine, Feb 02 2015

Status

approved