A212879 Decimal expansion of the absolute value of i!.

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

Offset

0,1

Comments

Also absolute value of Gamma(i).

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Formula

Equals abs(Gamma(i)), since i! = Gamma(1+i) = i*Gamma(i).

Equals sqrt(Pi/sinh(Pi)). - Vaclav Kotesovec, Dec 10 2015

Equals Product_{k>=1} k/sqrt(k^2+1) = sqrt(A090986). - Amiram Eldar, Oct 25 2024

Example

0.5215640468649398411581802696...

Mathematica

N[Sqrt[Pi/Sinh[Pi]], 103] (* Vaclav Kotesovec, Dec 10 2015 *)
RealDigits[Abs[I!], 10, 120][[1]] (* Amiram Eldar, Oct 25 2024 *)

Prog

(PARI) abs(gamma(I))

Crossrefs

Cf. A090986, A212877 (real(i!)), A212878 (-imag(i!)), A212880 (-arg(i!)).

Sequence in context: A091505 A366626 A030357 * A276524 A111395 A188596

Adjacent sequences: A212876 A212877 A212878 * A212880 A212881 A212882

Keyword

nonn,cons,easy

Author

Stanislav Sykora, May 29 2012

Status

approved