%I A113208
%S A113208 1,1,2,4,10,44,1426,17592187106356
%N A113208 Half-fixed-point of ascending descending base exponent transform.
%C A113208 a(9) has 429 digits. The ascending descending base exponent transform 
               applied to the Fibonacci numbers is A113122; applied to the tribonacci 
               numbers is A113153; applied to the Lucas numbers is A113154. There 
               is no nontrivial integer fixed point of the transform.
%F A113208 a(1) = 1. For n>1: a(n) = (1/2) * SUM[from i = 1 to n] (a(i))^a(n-i+1).
%e A113208 a(2) = 1 because a(1)^a(2) + a(2)^a(1) = 1^1 + 1^1 = 2 and 2/2 = 1.
%e A113208 a(3) = 2 because a(1)^a(3) + a(2)^a(2) + a(3)^a(1) = 1^2 + 1^1 + 2^1 
               = 4 and 4/2 = 2.
%e A113208 a(4) = 4 because a(1)^a(4) + a(2)^a(3) + a(3)^a(2) + a(4)^a(1) = 1^4 
               + 1^2 + 2^1 + 4^1 = 8 and 8/2 = 4.
%e A113208 a(5) = 10 because a(1)^a(5) + a(2)^a(4) + a(3)^a(3) + a(4)^a(2) + a(5)^a(1) 
               = 1^10 + 1^4 + 2^2 + 4^1 + 10^1 = 20 and 20/2 = 10.
%e A113208 a(6) = 44 because 1^44 + 1^10 + 2^4 + 4^2 + 10^1 + 44^1 = 88 and 88/2 
               = 44.
%e A113208 a(7) = (1^1426 + 1^44 + 2^10 + 4^4 + 10^2 + 44^1 + 1426^1)/2 = 1426.
%e A113208 a(8) = (1^17592187106356 + 1^1426 + 2^44 + 4^10 + 10^4 + 44^2 + 1426^1 
               + 17592187106356^1)/2 = 17592187106356.
%Y A113208 Cf. A113122, A113153, A113154.
%Y A113208 Sequence in context: A013549 A125805 A028404 this_sequence A000613 A053500 
               A080090
%Y A113208 Adjacent sequences: A113205 A113206 A113207 this_sequence A113209 A113210 
               A113211
%K A113208 easy,nonn
%O A113208 1,3
%A A113208 Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 06 2006