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

Author

Alois P. Heinz, Aug 29 2012

Keywords

• nonn
• more

Examples

			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.
		

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.

Programs

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);