A240984 Decimal expansion of the infinite product of e*(1-1/n^2)^(n^2) for n >= 2, which evaluates as Pi/e^(3/2).

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

Offset

0,1

Links

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

Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2024. See section 1.3, p.3.

S. R. Holcombe, A Product Representation of Pi, The American Mathematical Monthly, Vol. 120, No. 8 (2013), p. 705; arXiv preprint, arXiv:1204.2451 [math.NT], 2012-2020.

Formula

Product_{n>=2} e*(1-1/n^2)^(n^2) = Pi/e^(3/2).

Equals exp(-A389666). - Amiram Eldar, Jul 14 2026

Example

0.700984071916621199815471435765715490171309971900260379323128...

Mathematica

RealDigits[Pi/E^(3/2), 10, 100] // First

Prog

(PARI) Pi/exp(3/2) \\ Amiram Eldar, Jul 14 2026

Crossrefs

Cf. A389666.

Sequence in context: A388254 A344785 A390281 * A235363 A356592 A211904

Adjacent sequences: A240981 A240982 A240983 * A240985 A240986 A240987

Keyword

nonn,cons,easy,changed

Author

Jean-François Alcover, Aug 06 2014

Status

approved