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%I #10 Jul 10 2024 15:02:45
%S 1,15,131325321,
%T 210449029945495266124836624698709415244045199778210143675
%N Sequence of iterated increasing power sums. These sums are a generalization of iterated triangle sums.
%C These are iterated increasing power sums. These sums are a generalization of iterated triangle sums.
%F Let S(m, n) = Sum_{k=1...n} k^m; we define a(1):=S(1, 1), a(2):=S(1, S(2, 2)) etc., a(n):=S(1, S(2, S(3, ...S(n, n))...))).
%e a(1) = S(1,1)=1.
%e a(2) = S(1,S(2,2)) = S(1,5) = 15;
%e a(3) = S(1,S(2,S(3,3) = S(1,S(2,36) = S(1,16206) = 131325321.
%Y See A115243 for iterated decreasing power sums.
%K nonn
%O 1,2
%A _Hieronymus Fischer_, Jan 19 2006
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