A247444 Decimal expansion of the infinite product of (1-1/n^2)^(n^2)/(1-1/(4*n^2))^(4*n^2) for n >= 2.

7, 6, 1, 1, 9, 3, 8, 7, 8, 3, 4, 7, 6, 3, 2, 0, 7, 6, 0, 5, 2, 3, 7, 2, 5, 6, 3, 8, 9, 8, 5, 0, 6, 9, 9, 5, 1, 3, 9, 7, 1, 9, 1, 2, 0, 5, 3, 0, 9, 0, 6, 9, 8, 3, 7, 7, 0, 0, 2, 9, 3, 7, 3, 5, 1, 4, 1, 3, 5, 2, 0, 3, 0, 3, 9, 0, 7, 5, 9, 4, 0, 9, 5, 7, 6, 8, 2, 2, 5, 5, 7, 6, 2, 1, 2, 9, 2, 0, 0, 1

Offset

0,1

Links

Table of n, a(n) for n=0..99.

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 2.

S. R. Holcombe, A product representation for Pi, arXiv:1204.2451 [math.NT], 2012.

Formula

Equals (2^9/9^2)*Pi*exp(7*zeta(3)/(2*Pi^2)) = A240984 / A240985.

Example

0.76119387834763207605237256389850699513971912053...

Maple

evalf(product((1-1/n^2)^(n^2)/(1-1/(4*n^2))^(4*n^2), n=2..infinity), 100) # Vaclav Kotesovec, Sep 17 2014

Mathematica

RealDigits[(9^2/2^9)*Pi*Exp[7*Zeta[3]/(2*Pi^2)], 10, 100] // First

Crossrefs

Cf. A240984.

Sequence in context: A334400 A309700 A353823 * A319331 A371804 A010511

Adjacent sequences: A247441 A247442 A247443 * A247445 A247446 A247447

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 17 2014

Status

approved