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

0,1

Links

Table of n, a(n) for n=0..104.

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; p. 425-426.

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

Example

0.882542400610606373585825728471990763930758994918621881957052934828487068186...

Mathematica

1+(4*Log[2]-Pi)/Pi // N[#, 100]& // RealDigits // First

Prog

(PARI) 4*log(2)/Pi \\ Michel Marcus, Jul 28 2016

Crossrefs

Cf. A016639, A163973.

Sequence in context: A105193 A178678 A217459 * A344074 A377589 A011464

Adjacent sequences: A185277 A185278 A185279 * A185281 A185282 A185283

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 23 2013

Extensions

a(99) corrected by Georg Fischer, Jul 12 2021

Status

approved