

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
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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.


KEYWORD

nonn,more


AUTHOR



STATUS

approved



