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%I #9 May 18 2017 02:37:18
%S 1,2,4,8,17,54,472,27216,84738887,299164114847940,
%T 311903053042108587337426568,
%U 5846720173185251353387753850814872871131756204168
%N Sum of the first n tribonacci numbers, in ascending order, as bases, with the same, in descending order, as exponents.
%F a(n) = Sum_{i=1..n} (A000073(i))^A000073(n-i+1).
%e For the tribonacci sequence, starting t(1)=t(2)=1:
%e a(1) = t(1)^t(1) = 1^1 = 1.
%e a(2) = t(1)^t(2) + t(2)^t(1) = 1^1 + 1^1 = 2.
%e a(3) = t(1)^t(3) + t(2)^t(2) + t(3)^t(1) = 1^2 + 1^1 + 2^1 = 4.
%e a(4) = t(1)^t(4) + t(2)^t(3) + t(3)^t(2) + t(4)^t(1) = 1^4 + 1^2 + 2^1 + 4^1 = 8.
%e a(5) = 1^7 + 1^4 + 2^2 + 4^1 + 7^1 = 17.
%e a(6) = 1^13 + 1^7 + 2^4 + 4^2 + 7^1 + 13^1 = 54.
%e a(7) = 1^24 + 1^13 + 2^7 + 4^4 + 7^2 + 13^1 + 24^1 = 472.
%e a(8) = 1^44 + 1^24 + 2^13 + 4^7 + 7^4 + 13^2 + 24^1 + 44^1 = 27216.
%e a(9) = 1^81 + 1^44 + 2^24 + 4^13 + 7^7 + 13^4 + 24^2 + 44^1 + 81^1 = 84738887.
%e a(10) = 1^149 + 1^81 + 2^44 + 4^24 + 7^13 + 13^7 + 24^4 + 44^2 + 81^1 + 149^1 = 299164114847940.
%e a(11) = 1^274 + 1^149 + 2^81 + 4^44 + 7^24 + 13^13 + 24^7 + 44^4 + 81^2 + 149^1 + 274^1 = 311903053042108587337426568.
%e a(12) = 1^504 + 1^274 + 2^149 + 4^81 + 7^44 + 13^24 + 24^13 + 44^7 + 81^4 + 149^2 + 274^1 + 504^1 = 5846720173185251353387753850814872871131756204168.
%t a[0] = a[1] = 0 ; a[2] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3]; Table[Sum[a[k + 2]^(a[n - k + 1]), {k, 1, n}], {n, 1, 10}] (* _G. C. Greubel_, May 18 2017 *)
%Y Cf. A000073.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Jan 04 2006
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