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 A215971 Number of distinct values taken by 8th 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, 717, 1815, 4574, 11505, 28546, 69705, 166010 (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 8th derivative at x=1: (x^(x^(x^x))) -> 269128; ((x^x)^(x^x)), ((x^(x^x))^x) -> 382520; (x^((x^x)^x)) -> 511216; (((x^x)^x)^x) -> 646272. MAPLE # load programs from A215703, then: a:= n-> nops({map(f-> 8!*coeff(series(subs(x=x+1, f),                   x, 9), x, 8), T(n))[]}): seq(a(n), n=1..10); 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, A215838. Column k=8 of A216368. Sequence in context: A318801 A318854 A255638 * A034825 A145546 A292553 Adjacent sequences:  A215968 A215969 A215970 * A215972 A215973 A215974 KEYWORD nonn,more AUTHOR Alois P. Heinz, Aug 29 2012 STATUS approved

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Last modified September 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)