A115410 - OEIS (original) (raw)

COMMENTS

Can be understood as generalized iterated square pyramidal numbers. The growth of the sequence is bounded by O(n^3^n/3^(n/2)). This can be derived from the growth O(n^3/3) of the power two sum (1^2+2^2+3^2+...+n^2) by iteration.

FORMULA

Let T(n):=Sum_{k=1..n} k^2; we define a(1):=T(1), a(2):=T(T(2)) etc., a(n):=T(T(T(...(T(n))...))).

EXAMPLE

a(2) = T(T(2)) = T(5) = 55;

a(3) = T(T(T(3))) = T(T(14)) = T(1015) = 349074740.

MATHEMATICA

t[n_]:=Sum[k^2, {k, n}]; Table[Nest[t[#]&, n, n], {n, 5}] (* James C. McMahon, Aug 10 2024 *)