A330862 Decimal expansion of Product_{k>=1} (1 - 1/(-2)^k).

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

Offset: 1

Author

Ilya Gutkovskiy, Apr 28 2020

Keywords

• nonn
• cons

Examples

			(1 + 1/2) * (1 - 1/2^2) * (1 + 1/2^3) * (1 - 1/2^4) * (1 + 1/2^5) * ... = 1.2107241303010591801361728561...
		

Crossrefs

Cf. A000203, A048651, A065446, A079555, A081845, A085011, A100221, A132020, A330863.

Programs

Mathematica

RealDigits[QPochhammer[-1/2, -1/2], 10, 111] [[1]]
N[QPochhammer[-2, 1/4]*QPochhammer[1/4]/3, 120] (* Vaclav Kotesovec, Apr 28 2020 *)

PARI

prodinf(k=1, 1 - 1/(-2)^k) \\ Michel Marcus, Apr 28 2020

Formula

Equals Product_{k>=1} (4^k - 1)*(4^k + 2)/4^(2*k).

Equals exp(-Sum_{k>=1} A000203(k)/(k*(-2)^k)).