A225164 Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 5/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.

1, 4, 84, 45444, 15686405364, 2147492192737717340004, 45388476229808808857318702720533556450342484

Offset

1,2

Comments

Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165423(n+2), hence s(n) = sum(A165423(i+1)/A225157(i),i=1..n) = product(A165423(i+1)/A225157(i),i=1..n) = A165423(n+2)/a(n) = A176594(n-1)/a(n).

Links

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

Formula

a(n) = 5^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/5.

Example

f(n) = 5, 5/4, 25/21, 625/541, ...
5 + 5/4 = 5 * 5/4 = 25/4; 5 + 5/4 + 25/21 = 5 * 5/4 * 25/21 = 625/84; ...
s(n) = 1/b(n) = 5, 25/4, 625/84, ...

Maple

b:=proc(n) option remember; b(n-1)-b(n-1)^2; end:
b(1):=1/5;
a:=n->5^(2^(n-1))*b(n);
seq(a(i), i=1..8);

Crossrefs

Cf. A076628, A165423, A176594, A225157.

Sequence in context: A015018 A204245 A287248 * A229185 A360741 A184100

Adjacent sequences: A225161 A225162 A225163 * A225165 A225166 A225167

Keyword

nonn

Author

Martin Renner, Apr 30 2013

Status

approved