A185280 Decimal expansion of a constant appearing in the solution of Polya's 2D drunkard problem.
8, 8, 2, 5, 4, 2, 4, 0, 0, 6, 1, 0, 6, 0, 6, 3, 7, 3, 5, 8, 5, 8, 2, 5, 7, 2, 8, 4, 7, 1, 9, 9, 0, 7, 6, 3, 9, 3, 0, 7, 5, 8, 9, 9, 4, 9, 1, 8, 6, 2, 1, 8, 8, 1, 9, 5, 7, 0, 5, 2, 9, 3, 4, 8, 2, 8, 4, 8, 7, 0, 6, 8, 1, 8, 6, 7, 4, 6, 7, 2, 9, 9, 9, 1, 9, 7, 2, 4, 4, 7, 4, 1, 5, 8, 7, 0, 2, 2, 3, 5, 5, 4, 5, 9, 3
Offset: 0
Examples
0.882542400610606373585825728471990763930758994918621881957052934828487068186...
Links
- P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; p. 425-426.
Programs
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Mathematica
1+(4*Log[2]-Pi)/Pi // N[#, 100]& // RealDigits // First
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PARI
4*log(2)/Pi \\ Michel Marcus, Jul 28 2016
Formula
1 + Sum_{n>=1} binomial(2*n, n)^2/16^n - 1/(Pi*n).
Equals 1 + (4*log(2) - Pi)/Pi.
Equals 4*log(2)/Pi. - Michel Marcus, Jul 28 2016
Extensions
a(99) corrected by Georg Fischer, Jul 12 2021