A377764 Decimal expansion of (Pi/8)*exp(4*G/Pi), where G is the Catalan constant (A006752).

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

Offset

1,2

Links

Table of n, a(n) for n=1..90.

Michael Penn, A nice product from Ramanujan -- featuring 3 important constants!, YouTube video, 2023.

Formula

Equals A019675*A229728.

Equals Product_{k >= 1} (1 - 1/(2*k+1)^2)^((-1)^k*(2*k+1)) (from Ramanujan).

Equals Product_{k >= 1} (1 - 1/A016754(k))^((-1)^k*A005408(k)).

Example

1.26052961282938641055453633013540984220266923935...

Mathematica

First[RealDigits[Pi/8*Exp[4*Catalan/Pi], 10, 100]]

Crossrefs

Cf. A000796, A001113, A005408, A006752, A016754, A019675, A229728.

Sequence in context: A108431 A190144 A019967 * A336082 A327280 A350256

Adjacent sequences: A377761 A377762 A377763 * A377765 A377766 A377767

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 06 2024

Status

approved