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A241991 Decimal expansion of the infinite product for n >= 1 of (1+1/n^2)^(n^2)/e. 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, 6, 0, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..102.

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

FORMULA

p = exp(1/2 + 2*Pi/3 - 1/(2*Pi^2)*zeta(3) + 1/(2*Pi^2)*Li_3(exp(-2*Pi)) + (1/Pi)*Li_2(exp(-2*Pi)))/(2*sinh(Pi)), where Li_n is the n-th polylogarithm.

EXAMPLE

0.54578183883398708252349039725565877403368791329804393276759526235...

MATHEMATICA

p = Exp(1/2 + 2*Pi/3 - 1/(2*Pi^2)*Zeta(3) + 1/(2*Pi^2)*PolyLog(3, Exp(-2*Pi)) + (1/Pi)*PolyLog(2, Exp(-2*Pi)))/(2*Sinh(Pi)); RealDigits(p, 10, 103) // First

PROG

(PARI) exp(1/2 + 2*Pi/3 - zeta(3)/(2*Pi^2) + polylog(3, exp(-2*Pi))/(2*Pi^2) + polylog(2, exp(-2*Pi))/Pi)/2/sinh(Pi) \\ Charles R Greathouse IV, Aug 27 2014

(Python)

from mpmath import *

mp.dps=104

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

CROSSREFS

Cf. A240984.

Sequence in context: A119807 A254181 A245018 * A184306 A176317 A092426

Adjacent sequences:  A241988 A241989 A241990 * A241992 A241993 A241994

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Aug 11 2014

STATUS

approved

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