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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
OFFSET
1,3
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
KEYWORD
nonn,more
AUTHOR
Alois P. Heinz, Aug 29 2012
STATUS
approved