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A306679

a(n) = round(1/(1-Integral_{x=0..1} f_n(x) dx)), where f_n is the n-th of all functions that are representable as x^x^...^x with m>=1 x's and parentheses inserted in all possible ways.

2, 5, 10, 2, 17, 6, 2, 4, 26, 13, 3, 5, 8, 2, 2, 4, 2, 37, 21, 8, 11, 15, 3, 5, 5, 6, 9, 6, 2, 2, 3, 2, 2, 4, 4, 2, 3, 50, 32, 16, 3, 19, 23, 7, 11, 2, 4, 7, 10, 12, 16, 13, 2, 3, 6, 3, 5, 5, 7, 6, 5, 9, 8, 6, 8, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 5, 4, 3, 4, 4

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OFFSET

1,1

COMMENTS

The ordering of the functions f_n 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), ... . Values of new records are in A322008.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..20299

FORMULA

a(n) >= 2 for n >= 1.

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:

a:= proc() local i, l; i, l:= 0, []; proc(n) while n>

nops(l) do i:= i+1; l:= [l[], map(f-> round(evalf(