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

Author

Martin Renner, Apr 30 2013

Keywords

• nonn

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).

Examples

			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, ...
		

Crossrefs

Cf. A076628, A165423, A176594, A225157.

Programs

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);

Formula

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