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, 5, 155, 176855, 265770796655, 679134511201261085170655, 4943777738415359153962876938905400001585992709055

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