A225166 - OEIS

A225166

Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 7/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.

1, 6, 258, 552894, 2881632108858, 87461276190009420415561494, 88945179016152188483365571645414219233310820789054258

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OFFSET

1,2

COMMENTS

Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165425(n+2), hence sum(A165425(i+1)/A225159(i),i=1..n) = product(A165425(i+1)/A225159(i),i=1..n) = A165425(n+2)/a(n).

LINKS

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

FORMULA

a(n) = 7^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/7.

EXAMPLE

f(n) = 7, 7/6, 49/43, 2401/2143, ...

7 + 7/6 = 7 * 7/6 = 49/6; 7 + 7/6 + 49/43 = 7 * 7/6 * 49/43 = 2401/258; ...

s(n) = 1/b(n) = 7, 49/6, 2401/258, ...

MAPLE

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

b(1):=1/7;

a:=n->7^(2^(n-1))*b(n);