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A132267 Decimal expansion of Product_{k>0} (1-1/11^k). 4
9, 0, 0, 8, 3, 2, 7, 0, 6, 8, 0, 9, 7, 1, 5, 2, 7, 9, 9, 4, 9, 8, 6, 2, 6, 9, 4, 7, 6, 0, 6, 4, 7, 7, 4, 4, 7, 6, 2, 4, 9, 1, 1, 9, 2, 2, 1, 6, 6, 3, 9, 5, 2, 4, 0, 2, 1, 4, 6, 1, 7, 2, 4, 8, 8, 0, 6, 5, 7, 0, 8, 7, 0, 6, 7, 0, 9, 7, 5, 8, 5, 6, 7, 0, 0, 1, 6, 3, 9, 2, 9, 9, 1, 9, 9, 2, 8, 3, 5, 6, 4, 6, 5, 2, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2000

FORMULA

exp(-Sum_{n>0} sigma_1(n)/(n*11^n)) = exp(-Sum_{n>0} A000203(n)/(n*11^n)).

Equals (1/11; 1/11)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - G. C. Greubel, Dec 20 2015

EXAMPLE

0.900832706809715279949862694760...

MATHEMATICA

digits = 105; NProduct[1-1/11^k, {k, 1, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+3] // N[#, digits+3]& // RealDigits[#, 10, digits]& // First (* Jean-Fran├žois Alcover, Feb 18 2014 *)

N[QPochhammer[1/11, 1/11], 200] (* G. C. Greubel, Dec 20 2015 *)

PROG

(PARI) prodinf(x=1, 1-1/11^x) \\ Altug Alkan, Dec 20 2015

CROSSREFS

Cf. A000203, A048651, A100220, A132019-A132026, A132034-A132038, A132265-A132268, A132323-A132326.

Sequence in context: A257435 A296458 A199870 * A021115 A073052 A230068

Adjacent sequences:  A132264 A132265 A132266 * A132268 A132269 A132270

KEYWORD

nonn,cons

AUTHOR

Hieronymus Fischer, Aug 20 2007

STATUS

approved

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Last modified May 26 17:16 EDT 2020. Contains 334630 sequences. (Running on oeis4.)