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.

1, 1, 2, 4, 9, 20, 48, 115, 286, 717, 1815, 4574, 11505, 28546, 69705, 166010

Offset

1,3

Links

Table of n, a(n) for n=1..16.

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

Adjacent sequences: A215968 A215969 A215970 * A215972 A215973 A215974

Keyword

nonn,more

Author

Alois P. Heinz, Aug 29 2012

Status

approved