%I A113154
%S A113154 1,4,32,153,2798,197282,392458839,68701093784946,
%T A113154 26589104218033177611804,1824800382950333667240931155126914915,
%U A113154 48519278097695351677170017554626182187607010493656860644716
%N A113154 Sum of the first n Lucas numbers, in ascending order, as bases, with 
               the same, in descending order, as exponents.
%F A113154 a(n) = SUM[from i = 1 to n] (A000204(i))^A000204(n-i+1)
%e A113154 For the Lucas sequence, starting L(1)=1, L(2)=3:
%e A113154 a(1) = L(1)^L(1) = 1^1 = 1.
%e A113154 a(2) = L(1)^L(2) + L(2)^L(1) = 1^3 + 3^1 = 4.
%e A113154 a(3) = L(1)^L(3) + L(2)^L(2) + L(3)^L(1) = 1^4 + 3^3 + 4^1 = 32.
%e A113154 a(4) = L(1)^L(4) + L(2)^L(3) + L(3)^L(2) + L(4)^L(1) = 1^7 + 3^4 + 4^3 
               + 7^1 = 153.
%e A113154 a(5) = 1^11 + 3^7 + 4^4 + 7^3 + 11^1 = 2798.
%e A113154 a(6) = 1^18 + 3^11 + 4^7 + 7^4 + 11^3 + 18^1 = 197282.
%e A113154 a(7) = 1^29 + 3^18 + 4^11 + 7^7 + 11^4 + 18^3 + 29^1 = 392458839.
%e A113154 a(8) = 1^47 + 3^29 + 4^18 + 7^11 + 11^7 + 18^4 + 29^3 + 47^1 = 68701093784946.
%e A113154 a(9) = 1^76 + 3^47 + 4^29 + 7^18 + 11^11 + 18^7 + 29^4 + 47^3 + 76^1 
               = 26589104218033177611804.
%e A113154 a(10) = 1^123 + 3^76 + 4^47 + 7^29 + 11^18 + 18^11 + 29^7 + 47^4 + 76^3 
               + 123^1 = 1824800382950333667240931155126914915.
%e A113154 a(11) = 1^199 + 3^123 + 4^76 + 7^47 + 11^29 + 18^18 + 29^11 + 47^7 + 
               76^4 + 123^3 + 199^1 = 48519278097695351677170017554626182187607010493656860644716.
%Y A113154 Cf. A000204.
%Y A113154 Sequence in context: A088802 A123854 A112850 this_sequence A083299 A018215 
               A099133
%Y A113154 Adjacent sequences: A113151 A113152 A113153 this_sequence A113155 A113156 
               A113157
%K A113154 easy,nonn
%O A113154 1,2
%A A113154 Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 05 2006