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 A306726 a(n) = Sum_{i=1..n} f_i(0), where f_i is the i-th of all functions that are representable as x^x^...^x with m>=1 x's and parentheses inserted in all possible ways, with conventions that 0^0=1^0=1^1=1, 0^1=0. 3
 0, 1, 2, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 9, 9, 10, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 20, 20, 21, 21, 21, 22, 23, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 31, 32, 33, 34, 34, 35, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 47, 47, 47, 47 (list; graph; refs; listen; history; text; internal format)
 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 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 Partial sums of A306710. Cf. A000081, A087803, A215703. Sequence in context: A237638 A334483 A261093 * A188511 A064488 A049472 Adjacent sequences:  A306723 A306724 A306725 * A306727 A306728 A306729 KEYWORD nonn AUTHOR Alois P. Heinz, Mar 06 2019 STATUS approved

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Last modified September 23 21:27 EDT 2020. Contains 337315 sequences. (Running on oeis4.)