login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A245018 Decimal expansion of the infinite product of (1+1/n^2)^(n^2)/e for n >= 1. 0
5, 4, 5, 7, 8, 1, 8, 3, 8, 8, 3, 3, 9, 8, 7, 0, 8, 2, 5, 2, 3, 4, 9, 0, 3, 9, 7, 2, 5, 5, 6, 5, 8, 7, 7, 4, 0, 3, 3, 6, 8, 7, 9, 1, 3, 2, 9, 8, 0, 4, 3, 9, 3, 2, 7, 6, 7, 5, 9, 5, 2, 6, 2, 3, 5, 0, 6, 1, 8, 4, 4, 6, 8, 7, 4, 1, 0, 8, 4, 0, 5, 2, 5, 1, 2, 7, 0, 3, 1, 0, 6, 0, 2, 6, 1, 0, 0, 3, 0, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 3.

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

FORMULA

exp(1/2 + 2*Pi/3 - zeta(3)/(2*Pi^2) + Li_3(e^(-2*Pi))/(2*Pi^2) + Li_2(e^(-2*Pi))/Pi)/(2*sinh(Pi)).

EXAMPLE

0.545781838833987082523490397255658774033687913298...

MAPLE

evalf(product((1+1/n^2)^(n^2)/exp(1), n=1..infinity), 120) # Vaclav Kotesovec, Sep 17 2014

MATHEMATICA

p = Exp[1/2 + 2*Pi/3 - Zeta[3]/(2*Pi^2) + PolyLog[3, E^(-2*Pi)]/(2*Pi^2) + PolyLog[2, E^(-2*Pi)]/Pi]/(2*Sinh[Pi]); RealDigits[p, 10, 100] // First

PROG

(Python)

from mpmath import *

mp.dps=101

print map(int, list(str(exp(1/2 + 2*pi/3 - zeta(3)/(2*pi**2) + polylog(3, e**(-2*pi))/(2*pi**2) + polylog(2, e**(-2*pi))/pi)/(2*sinh(pi)))[2:-1])) # Indranil Ghosh, Jul 03 2017

CROSSREFS

Cf. A240984, A247444.

Sequence in context: A069214 A119807 A254181 * A241991 A184306 A176317

Adjacent sequences:  A245015 A245016 A245017 * A245019 A245020 A245021

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Sep 17 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 10 10:17 EDT 2020. Contains 335576 sequences. (Running on oeis4.)