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.

1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1838, 4734, 12247, 31617, 81208

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