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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
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
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.)