A216403 Number of distinct values taken by 10th 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, 1842, 4763, 12452, 32711, 86239

Offset

1,3

Links

Table of n, a(n) for n=1..15.

Example

a(4) = 4 because the A000108(3) = 5 possible parenthesizations of x^x^x^x lead to 4 different values of the 10th derivative at x=1: (x^(x^(x^x))) -> 37616880; ((x^x)^(x^x)), ((x^(x^x))^x) -> 42409440; (x^((x^x)^x)) -> 77899320; (((x^x)^x)^x) -> 66712680.

Maple

# load programs from A215703, then:
a:= n-> nops({map(f-> 10!*coeff(series(subs(x=x+1, f),
                  x, 11), x, 10), 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, A215840. Column k=10 of A216368.

Sequence in context: A318803 A318856 A255640 * A145548 A292555 A318804

Adjacent sequences: A216400 A216401 A216402 * A216404 A216405 A216406

Keyword

nonn

Author

Alois P. Heinz, Sep 06 2012

Status

approved