OFFSET
1,2
COMMENTS
These are iterated increasing power sums. These sums are a generalization of iterated triangle sums.
FORMULA
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))...))).
EXAMPLE
a(1) = S(1,1) = 1.
a(2) = S(1,S(2,2)) = S(1,5) = 15.
a(3) = S(1,S(2,S(3,3))) = S(1,S(2,36)) = S(1,16206) = 131325321.
CROSSREFS
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Jan 19 2006
STATUS
approved