1,2

There are an infinite number of sequences {a(k)}, with different values for a(1) and a(2) (a(1) must be 0 or 1; a(2) can be anything), where product{k=1 to n} (sum{j=1 to k} a(j)) = sum{k=1 to n} product{j=1 to k} a(j), for all positive integers n. Setting a(1) to 1 and a(2) to 2 results in the sequence here.

For n >= 4, a(n) = -2^(2^(n-3)) * (2^(2^(n-3)) - 1).

For n = 4, we have a(1) * (a(1)+a(2)) * (a(1)+a(2)+a(3)) * (a(1)+a(2)+a(3)+a(4)) = a(1) + a(1)*a(2) + a(1)*a(2)*a(3) + a(1)*a(2)*a(3)*a(4) =

1 * (1+2) * (1+2-6) * (1+2-6-12) = 1 + 1*2 + 1*2*(-6) + 1*2*(-6)*(-12) = 135.

Sequence in context: A089423 A062349 A105122 this_sequence A058046 A074180 A126293

Adjacent sequences: A132073 A132074 A132075 this_sequence A132077 A132078 A132079

easy,more,sign

Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Oct 30 2007