%I #5 Apr 30 2013 13:24:07
%S 1,1,2,1,2,5,2,1,2,5,15,5,2,5,2,1,2,5,15,5,15,52,15,5,2,5,15,5,2,5,2,1
%N Rows of triangle A165194 tend to this sequence; generated from A000110.
%F The sequence can be generated from strings of 2^n terms starting (1, 1,... then the next string of 2^(n+1) terms is obtained by appending a "reverse and increment" substring to the previous substring.
%e Given terms in the Bell sequence, A000110; A165195 begins (1, 1, 2, 1,... then to obtain the first 2^3 terms, the first 2^2 terms = (1, 1, 2, 1,... then append to the latter the reversal of (1, 1, 2, 1) = (1, 2, 1, 1) but incremented with the next higher Bell number = (2, 5, 2, 1). The first 2^3 terms are thus (1, 1, 2, 1, 2, 5, 2, 1). Repeat with analogous operations to obtain 2^4 terms, and so on..
%Y Cf. A000110, A165194, A165196.
%K nonn
%O 1,3
%A _Gary W. Adamson_, Sep 06 2009