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A100221 Decimal expansion of Product_{k>=1} (1-1/4^k). 12
6, 8, 8, 5, 3, 7, 5, 3, 7, 1, 2, 0, 3, 3, 9, 7, 1, 5, 4, 5, 6, 5, 1, 4, 3, 5, 7, 2, 9, 3, 5, 0, 8, 1, 8, 4, 6, 7, 5, 5, 4, 9, 8, 1, 9, 3, 7, 8, 3, 3, 5, 7, 3, 5, 3, 4, 0, 1, 5, 7, 2, 3, 2, 5, 7, 7, 5, 3, 3, 1, 9, 8, 4, 5, 0, 7, 9, 8, 6, 7, 5, 1, 2, 4, 8, 0, 3, 3, 4, 6, 0, 4, 8, 1, 4, 2, 8, 8, 7, 9, 0, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1200

Eric Weisstein's World of Mathematics, Infinite Product

Eric Weisstein's World of Mathematics, q-Pochhammer Symbol

FORMULA

Equals exp(-Sum_{k>0} sigma_1(k)/(k*4^k)) where sigma_1() is A000203(). - Hieronymus Fischer, Aug 07 2007

Equals (1/4; 1/4)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - G. C. Greubel, Nov 30 2015

EXAMPLE

0.688537537...

MATHEMATICA

EllipticThetaPrime[1, 0, 1/2]^(1/3)/2^(1/4)

N[QPochhammer[1/4]] (* G. C. Greubel, Nov 30 2015 *)

PROG

(PARI) prodinf(x=1, 1-1/4^x) \\ Altug Alkan, Dec 01 2015

CROSSREFS

Cf. A027637, A048651, A100220, A100222.

Cf. A000203, A100220, A100222, A132020, A132034, A132035, A132036, A132037, A132038, A258459.

Sequence in context: A176104 A011481 A212480 * A157683 A300897 A049110

Adjacent sequences:  A100218 A100219 A100220 * A100222 A100223 A100224

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Nov 09 2004

STATUS

approved

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Last modified June 15 22:19 EDT 2019. Contains 324145 sequences. (Running on oeis4.)