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 A216062 Number of distinct values taken by 9th derivative of x^x^...^x (with n x's and parentheses inserted in all possible ways) at x=1. 2
 1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1838, 4734, 12247, 31617, 81208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(4) = 4 because the A000108(3) = 5 possible parenthesizations of x^x^x^x lead to 4 different values of the 9th derivative at x=1: (x^(x^(x^x))) -> 3010680; ((x^x)^(x^x)), ((x^(x^x))^x) -> 3863808; (x^((x^x)^x)) -> 6019416; (((x^x)^x)^x) -> 6333336. LINKS Table of n, a(n) for n=1..15. MAPLE # load programs from A215703, then: a:= n-> nops({map(f-> 9!*coeff(series(subs(x=x+1, f), x, 10), x, 9), T(n))[]}): seq(a(n), n=1..11); CROSSREFS 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, A215839. Column k=9 of A216368. Sequence in context: A318802 A318855 A255639 * A034826 A145547 A292554 Adjacent sequences: A216059 A216060 A216061 * A216063 A216064 A216065 KEYWORD nonn,more AUTHOR Alois P. Heinz, Aug 31 2012 STATUS approved

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Last modified May 25 05:18 EDT 2024. Contains 372782 sequences. (Running on oeis4.)