OFFSET
1,3
COMMENTS
The ordering of the functions f_i is defined in A215703: f_1, f_2, ... = x, x^x, x^(x^2), x^(x^x), x^(x^3), x^(x^x*x), x^(x^(x^2)), x^(x^(x^x)), x^(x^4), x^(x^x*x^2), ... .
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..53272
Alois P. Heinz, Animation of scaled plots [n/j-> a(n)/a(j)] for n = 1..j, and j = A087803(2)..A087803(15)
Wikipedia, Zero to the power of zero
FORMULA
a(n) = Sum_{i=1..n} A306710(i).
MAPLE
T:= proc(n) T(n):=`if`(n=1, [x], map(h-> x^h, g(n-1$2))) end:
g:= proc(n, i) option remember; `if`(i=1, [x^n], [seq(seq(
seq(mul(T(i)[w[t]-t+1], t=1..j)*v, v=g(n-i*j, i-1)), w=
combinat[choose]([$1..nops(T(i))+j-1], j)), j=0..n/i)])
end:
b:= proc() local i, l; i, l:= 0, []; proc(n) while n>nops(l)
do i:= i+1; l:= [l[], subs(x=0, T(i))[]] od; l[n] end
end():
a:= proc(n) option remember; `if`(n<1, 0, b(n)+a(n-1)) end:
seq(a(n), n=1..120);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 06 2019
STATUS
approved