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A225165 Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 6/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal. 1
1, 5, 155, 176855, 265770796655, 679134511201261085170655, 4943777738415359153962876938905400001585992709055 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165424(n+2), hence sum(A165424(i+1)/A225158(i),i=1..n) = product(A165424(i+1)/A225158(i),i=1..n) = A165424(n+2)/a(n) = A173501(n+2)/a(n).

LINKS

Table of n, a(n) for n=1..7.

FORMULA

a(n) = 6^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/6.

EXAMPLE

f(n) = 6, 6/5, 36/31, 1296/1141, ...

6 + 6/5 = 6 * 6/5 = 36/5; 6 + 6/5 + 36/31 = 6 * 6/5 * 36/31 = 1296/155; ...

s(n) = 1/b(n) = 6, 36/5, 1296/155, ...

MAPLE

b:=proc(n) option remember; b(n-1)-b(n-1)^2; end:

b(1):=1/6;

a:=n->6^(2^(n-1))*b(n);

seq(a(i), i=1..8);

CROSSREFS

Cf. A076628, A165424, A173501, A225158.

Sequence in context: A265123 A237527 A015019 * A151577 A032391 A139978

Adjacent sequences:  A225162 A225163 A225164 * A225166 A225167 A225168

KEYWORD

nonn

AUTHOR

Martin Renner, Apr 30 2013

STATUS

approved

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Last modified May 25 15:54 EDT 2022. Contains 354071 sequences. (Running on oeis4.)