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 A215796 Number of distinct values taken by 7th derivative of x^x^...^x (with n x's and parentheses inserted in all possible ways) at x=1. 3
 1, 1, 2, 4, 9, 20, 48, 115, 283, 691, 1681, 3988, 9241, 20681, 44217, 89644 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS EXAMPLE a(4) = 4 because the A000108(3) = 5 possible parenthesizations of x^x^x^x lead to 4 different values of the 7th derivative at x=1: (x^(x^(x^x))) -> 26054; ((x^x)^(x^x)), ((x^(x^x))^x) -> 41090; (x^((x^x)^x)) -> 47110; (((x^x)^x)^x) -> 70098. 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: f:= proc() local i, l; i, l:= 0, []; proc(n) while n>       nops(l) do i:= i+1; l:= [l[], T(i)[]] od; l[n] end     end(): a:= n-> nops({map(f-> 7!*coeff(series(subs(x=x+1, f), x, 8), x, 7), T(n))[]}): seq(a(n), n=1..12); CROSSREFS Column k=7 of A216368. Cf. A000081 (distinct functions), A000108 (parenthesizations), A000012 (first derivatives), A028310 (2nd derivatives), A199085 (3rd derivatives), A199205 (4th derivatives), A199296 (5th derivatives), A199883 (6th derivatives), A002845, A003018, A003019, A145545, A145546, A145547, A145548, A145549, A145550, A082499, A196244, A198683, A215703, A215837. Sequence in context: A318800 A318853 A255637 * A034824 A145545 A182378 Adjacent sequences:  A215793 A215794 A215795 * A215797 A215798 A215799 KEYWORD nonn,more AUTHOR Alois P. Heinz, Aug 24 2012 STATUS approved

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